# Structural Damping Examples

Structural damping enables you to incorporate hysteretic behavior due to internal material friction by specifying a coefficient on the stiffness matrix. From the structural point of view, the main sources of damping in a wing are the friction in joints, viscous damping due to air flow and material damping. Thus, structural damping is suggested for models involving materials that exhibit frictional behavior or where local frictional effects are present throughout the model, such as dry rubbing of joints in a multi-link structure. Introduction Damping is the energy dissipation of a material or system under cyclic stress. A common example of damping is shock absorbers on a vehicle. As our example, we will take the response of a bell, which is a lightly damped structure. LINEAR VISCOUS DAMPING Linear Viscous Damping Is a Property of the Computational Model And is not a Property of a Real Structure 19. 05 ) at the first natural frequency of the structure ( ω i = ω 1), and at ω j = 188. d : Damping ratio due to vibration control devices ÖNORM B4014 Teil 1, Code for Austria Wind (Actual Wind Load Code for Austria) 1st mode damping ratio ζ 1 (%) ζ 1 = ζ m + ζ c + ζ f ζ m: Structural damping ratio due to materials (%) 0. This is the more common understand-ing of modal damping. Get a demo of damping in action. Structural Dynamics D. Define damping. Structural Damping Structural damping reduces both impact-generated and steady-state noises at their source. All systems will posses some fundamental damping property. ) Case (iii) Critical Damping (repeated real roots) If b2 = 4mk then the term under the square root is 0 and the characteristic. These parameters consist of structural and damping indicators. Explain the purpose of damping. Taking a different approach, Structural Damping: Applications in Seismic Response Modification considers the dynamic responses of structures with added damping devices as systems governed by the combined effect of the static stiffness, period, and damping—or "dynamic stiffness"—of the structure-device system. Example sentences with "structural damping", translation memory patents-wipo The present invention is a conductive isolator including a damping structure , a conductive bridge component positioned within the damping structure , axial contact points between the damping structure and the conductive bridge component and radial contact points. modal parameters and monitor the structural response under strong wind conditions. San Jose, California. Parametric Sensitivity of Damped Systems. A damping coefficient is a material property that indicates whether a material will bounce back or return energy to a system. AREA = ENERGY DISSIPATED The force-displacement relationship for a linear viscous damper is an ellipse. Shock absorbers in automobiles and carpet pads are examples of damping devices. Chapter 12: Seismically Isolated Structures 12-3 isolators (and supplementary damping devices) could have been used equally well in the example. Define a free damped oscillation. A major part of the book is devoted to damping of structures and many sources of damping are considered, as are the ways of changing damping using both active and passive methods. In structural design against dynamic loads, damping is perhaps the least understood aspect. This reduction corresponds to increasing the basic structural damping by 4%. method is to increase the structural damping. Viscoelastic Damping System:In a system similar to a Viscous Damping system, the use of viscoelastic damping material, such as rubber, has been used for some applications. Mass, Stiffness, and Damping Matrix Estimates from Structural Measurements. x(t) = sin. Because damping in typical structures is small, approximations have been made to facilitate the design process with negligible effects. Structural Damping Structural damping reduces both impact-generated and steady-state noises at their source. Explain the purpose of damping. At first, a discrete model of the stay cable with an NSD attached perpendicularly near the support is established. Chapter 6 - Viscous & Viscoelastic Dampers CIE 626 - Structural Control Chapter 6 - Viscous-Viscoelastic Dampers 1. This is primarily due to the reality of variable loading on these types of systems. In structural systems, damping is more complex, appearing in several forms. The use of even small amounts of damping in computational models involving nonlinear plastic response can significantly influence the response calculations. Structural Measurement Systems, Inc. Shearing action of a rubber compound placed. Build model 2. AB - This paper considers a passive damping method that can be applied to a wide range of structural geometries including machine tool bases and components. ωt, and (8) v(t) =x (t) =ωcos ωt (9) The resulting coulomb damping force is obviously a square wave of period. We'll also go over some specific examples. Example(s): * Instruments such as speedometers are critically damped so when a car accelerates, the sp. o In tall buildings, bridges, vehicle guideways, and many other civil engineering structures and in machinery, such as robots and vehicles, dominant damping is the structural damping mechanism. Gavin Fall 2018 1 Preliminaries This document describes the formulation of stiﬀness and mass matrices for structural elements such as truss bars, beams, plates, and cables(?). Thus, structural damping is suggested for models involving materials that exhibit frictional behavior or where local frictional effects are present throughout the model, such as dry rubbing of joints in a multi-link structure. To investigate the effect/difference of damping, I have assigned a constant damping value of very high 20% to all components of the brake model (4 pieces). Modelling of damping is a very difficult issue because the level of damping in a structure can depend, for example, on the material damping that is dependent on the type of the. The friction between the beams is the dominant dynamical phenomenon. COMSOL Multiphysics provides you with a broad range of options for describing damping. and therefore it is difficult to predict. 0) to check intermediate ductility detail requirements. Let us begin with a review of how structural response can be represented in different domains. In the next section these methods will be illustrated using application examples from projects. Lower-limit values of the structural damping ratio for suspension and cable stayed bridge vibration modes driven by the cables are systematized in Table 21. Contents 1. • Use FSI to determine air damping. ) Case (iii) Critical Damping (repeated real roots) If b2 = 4mk then the term under the square root is 0 and the characteristic. As our example, we will take the response of a bell, which is a lightly damped structure. In order to do so, guidelines on how to estimate this load is indicated in each local code provision. Therefore, this form of damping can be used only when the displacement and velocity are exactly 90° out of phase. In other cases, we might be a member of the design-build team along with the fabricator and installer, reporting to the general contractor. Here, \omega_0 is the undamped natural frequency and \zeta is called the damping ratio. Structural Engineering and the Edexcel HNC/D module Mechanical Science. • In high-rise buildings, wind excitation can cause an oscillatory motion which is detrimental for comfort of the inhabitants in the top levels. San Jose, California. external means, such as joint friction, air damping and absorbers (structural damping or system damping), or by intrinsic means, including the use of suitable high- damping materials (material damping). The skillful application of the methods and analysis tools of structural dynamics is of paramount importance in the design of land, sea, air, and space vehicles. In particular, the method suggested by Ashby is applied, focusing on material weight reduction and stiffness increase [42,43,44]. All models show that large damping coefficients lead to locally over-damped responses. A major part of the book is devoted to damping of structures and many sources of damping are considered, as are the ways of changing damping using both active and passive methods. A method to deal with general asymmetric systems is described in the appendix. …If you don't have SolidWorks 2018 or later,…then you can use the para solid file, which is. (2006) "Problems encountered from the use (or misuse) of Rayleigh damping," Earthquake Engineering and Structural Dynamic, 35, 525-545 DOI EXAMPLE: rayleigh 0. -3- For purely viscous damping, which is easy to analyse theoretically,. This is a good example of a paradox at work, that is, a structure that is stiff yet flexible when required to be so as to be able to provide structural damping against earthquakes. A thin steel beam may be highly resonant and exhibit large vibration that cause fatigue and failure, or transmit vibration to other parts of the structure. The damping capacity is defined as the ratio of the. This example shows how to include damping in the transient analysis of a simple cantilever beam. We used two performance measures: the damping density and the damping cost of the device. 72 (RC with cracks), 0. For a frequency response model with damping, the results are complex. All models show that large damping coefficients lead to locally over-damped responses. This is the more common understand-ing of modal damping. (3) Rayleigh damping coefficients can be determined by the orthogonality of a damping matrix for a modal shape. No one would want to live in a building easily swayed by gust. Use the abs and angle functions to obtain real-valued magnitude and phase, respectively. equipment may also effect some improvement. These structures are also more vulnerable to earthquake excitation. • Note: Resulting simulation involves coupling of electrical, structural, and fluidic. Background on Vibration Damping Vibration Damping Background. Structural Vibration: Analysis and Damping benefits from my earlier book Structural Vibration Analysis: Modelling, Analysis and Damping of Vibrating Structures which was published in 1983 but is now out of print. We have to double check structural damping's off, Rayleigh damping's not on. This formulation supplies. 2 An Initial Numerical Example If we consider a spring-mass system as shown in Figure 1. The numerous worked examples liberally distributed throughout the text, amplify and clarify the theoretical analysis presented. Because it's difficult to analytically calculate the exact amount of damping in most structural and mechanical systems, the. Define damping ratio. For many purposes the damping force F f can be modeled as being proportional to the velocity v of the object: = −, where c is the damping coefficient, given in units of Newton-seconds per meter. We first give a damping design method and interface whereby the user can set the damping properties so that motion aligned with each of a few chosen example deformations is damped by an independently prescribed amount, whereas the rest of the deformation space follows standard Rayleigh damping, or any viscous damping. Introduction to Damping Models and Analysis Methods. Each of these mechanisms is analyzed to em-phasize the factors important in the utilization of damping as an engineering property. Knowledge of the level of damping in a dynamic system is important in the utilisation, analysis, and testing of the system. In addition to the Standard and the Provisions, the following documents are either referenced directly,. The main advantage of classical viscous damping model (for example Rayleigh model) is that the orthogonality of the modes is preserved; based on that the classical modal analysis will be, to some extent, similar to the un-damped vibration and easier in analysis. Hence, the equivalent viscous damping constant for Coulomb friction is given by C c= 4F c ˇ!X (13) 2. Enhanced damping value protects the structural system. Define a free damped oscillation. The damping capacity is defined as the ratio of the. One end of the double beam is ﬁxed. 6 is in fact equal to one half of the damping factor appropriate to the resonance frequency. For low values of damping (<2%), the structural amplification is over 25x, which indicates that even a low level of crowd force may cause a large acceleration response. 1 Structural Optimization Techniques. Use the abs and angle functions to obtain real-valued magnitude and phase, respectively. Because damping in typical structures is small, approximations have been made to facilitate the design process with negligible effects. Let us begin with a review of how structural response can be represented in different domains. This method is by far the simplest way to take care of vibrations in machinery. Each mechanical system from actuator to end-effector comprises structural damping. Examples are friction losses at any connection to or in the system and internal energy losses of the materials due to thermo-elasticity, hysteresis and inter-granular bonds. Described are six methods of extracting damping from data: the half-power. There are only a few examples of time-domain optimizations considering ﬂut-ter in the literature. Structural Vibration Fundamentals Free vibration and forced vibration Analysis models for structural dynamic systems Types of damping Types of dynamic forces Representation of dynamic forces in the time and frequency do-mains. This enhanced successor is far more comprehensive with more analytical discussion, further consideration of damping sources. Example sentences with "structural damping", translation memory patents-wipo The present invention is a conductive isolator including a damping structure , a conductive bridge component positioned within the damping structure , axial contact points between the damping structure and the conductive bridge component and radial contact points. Viscoelastic Damping System:In a system similar to a Viscous Damping system, the use of viscoelastic damping material, such as rubber, has been used for some applications. Therefore, damping input shows an enhanced accuracy and a reduced calculation scale. Here, \omega_0 is the undamped natural frequency and \zeta is called the damping ratio. Underdamped Oscillator. Damping, however, suppresses only resonant motion. Chapter 10 gives some tools for the quantiﬁcation of damping. Use features like bookmarks, note taking and highlighting while reading Structural Damping: Applications in Seismic Response. set it in motion) we would observe the system oscillating as shown in Figure 1. Although a non-damped. Structural Damping: Applications in Seismic Response Modification (Advances in Earthquake Engineering Book 3) - Kindle edition by Liang, Zach, Lee, George C. Modelling of damping is a very difficult issue because the level of damping in a structure can depend, for example, on the material damping that is dependent on the type of the. References. not clearly defined for the mode superposition transient analysis. method is to increase the structural damping. The book is written from a vibration theory standpoint, with numerous worked examples which are relevant across a wide range of mechanical, aerospace and structural engineering applications. detailed examples of the application of auxiliary damping devices in Australia, Canada, China, Japan, and the United States. 05 • All the components bolted to the structure (e. In terms of accuracy, there is very little difference between using 1 spline to connect the aerodynamic and structural DOF, and dividing the wing into two regions (such as an outer wing and an inner wing section) and using two splines. In such a case where. Hysteretic damping within the structural materials. A major part of the book is devoted to damping of structures and many sources of damping are considered, as are the ways of changing damping using both active and passive methods. Suppose the car drives at speed V over a road with sinusoidal roughness. The damping discussion may indicate that all structures with damping require damped free vibration analysis. 6 is in fact equal to one half of the damping factor appropriate to the resonance frequency. We have to double check structural damping's off, Rayleigh damping's not on. x(t) = sin. Damping, however, suppresses only resonant motion. For this reason a major part of the book is devoted to the damping of structural vibrations. Most frequently used in vibration analysis is viscous damping because it is. It was mounted in the base of the mast to achieve the School of Astronautics, Beihang University, Beijing, P. 0 Introduction The race toward new heights has not been without its challenges. In structural design against dynamic loads, damping is perhaps the least understood aspect. When the bell is struck, it. Because e−t goes to 0 more slowly than e−3t/2 it controls the rate at which x goes to 0. In this type of damping, the damping force is proportional to the displacement rather than the velocity as in the other damping options. Structural dynamics is a type of structural analysis which covers the behavior of a structure subjected to dynamic (actions having high acceleration) loading. 1a) pressed together by one or more bolted joints. Thus, structural damping is suggested for models involving materials that exhibit frictional behavior or where local frictional effects are present throughout the model, such as dry rubbing of joints in a multi-link. Ken Shye and Mark Richardson. reducing structural vibration. Forced, nonreso-nant vibration is rarely attenuated. Use features like bookmarks, note taking and highlighting while reading Structural Damping: Applications in Seismic Response. Damping, in physics, restraining of vibratory motion, such as mechanical oscillations, noise, and alternating electric currents, by dissipation of energy. The second argument must be 'proportional'. The use of even small amounts of damping in computational models involving nonlinear plastic response can significantly influence the response calculations. Dynamic Behavior of a Structural Component:. The utility of this passive damping technique is demonstrated experimentally, and examples showing the accuracy of the modal strain energy solution are presented. Damping, however, suppresses only resonant motion. , Dargush, Gary F. Structural damping is a measure of energy dissipation in a vibrating structure that results in bringing the structure to a quiescent state. Because damping in typical structures is small, approximations have been made to facilitate the design process with negligible effects. INTRODUCTION The response of buildings to earthquake ground shaking is a complex process. Structural Engineering and the Edexcel HNC/D module Mechanical Science. damping definition: nounThe gradual reduction of excessive oscillation, vibration, or signal intensity, and therefore of instability in a mechanical or electrical device, by a substance or some aspect of the device. This is the more common understand-ing of modal damping. • Particularly true with small air gap = electrostatic gap of 3 µm. The damping discussion may indicate that all structures with damping require damped free vibration analysis. Introduction to Structural Dynamics 1 Examples of dynamics in structures are: is the damping ratio which is the ratio of the damping coefficient, c, to the critical value of the damping coefficient ccr; we will see what these terms physically mean. Structural integrity and comfort are therefore compromised. In structural design against dynamic loads, damping is perhaps the least understood aspect. 3D Frame, 3-story 3-bayX 3-bayZ, Reinforced-Concrete Section & Steel W-Section. China Corresponding author:. A major part of the book is devoted to damping of structures and many sources of damping are considered, as are the ways of changing damping using both active and passive methods. Ken Shye and Mark Richardson. Damping characteristics of a structure could be improved by addition of additional damping devices, Dampers; at the strategic locations within the structure; which could be very. Hence, the equivalent viscous damping constant for Coulomb friction is given by C c= 4F c ˇ!X (13) 2. 016 Hz produced the spectrum shown as a dashed line in Figure 1. radiation damping - energy radiation into the surrounding medium. The damping discussion may indicate that all structures with damping require damped free vibration analysis. The numerous worked examples liberally distributed throughout the text, amplify and clarify the theoretical analysis presented. In such a case where. Addeddate 2015-09-02 21:19:26 Identifier StructuralVibrationAnalysisAndDampingC. Chapter 6 - Viscous & Viscoelastic Dampers CIE 626 - Structural Control Chapter 6 - Viscous-Viscoelastic Dampers 1. When the materials are deformed, energy is absorbed and dissipated by the material itself. The structural damping of a tower can be increased by the application of a damping pad, as shown in Figure 3. From the structural point of view, the main sources of damping in a wing are the friction in joints, viscous damping due to air flow and material damping. This is a good example of a paradox at work, that is, a structure that is stiff yet flexible when required to be so as to be able to provide structural damping against earthquakes. TOPIC 6 Structural Dynamics III Analysis of Elastic MDOF Systems. • In high-rise buildings, wind excitation can cause an oscillatory motion which is detrimental for comfort of the inhabitants in the top levels. Knowledge of the level of damping in a dynamic system is important in the utilisation, analysis, and testing of the system. For a frequency response model with damping, the results are complex. No one would want to live in a building easily swayed by gust. In order to do so, guidelines on how to estimate this load is indicated in each local code provision. When the bell is struck, it. Structural Vibration: Analysis and Damping benefits from my earlier book Structural Vibration Analysis: Modelling, Analysis and Damping of Vibrating Structures which was published in 1983 but is now out of print. Therefore, this form of damping can be used only when the displacement and velocity are exactly 90° out of phase. - [Instructor] This video shows setting up…and running a Transient Response Analysis. A thin steel beam may be highly resonant and exhibit large vibration that cause fatigue and failure, or transmit vibration to other parts of the structure. The main advantage of classical viscous damping model (for example Rayleigh model) is that the orthogonality of the modes is preserved; based on that the classical modal analysis will be, to some extent, similar to the un-damped vibration and easier in analysis. In structural dynamics the equilibrium of a vibrating system is usually described by a set of ordinary differential equations in the following form (see Clough, 1979, for example) M X"(t) + C X'(t) + K X(t) = F(t) (1. A major part of the book is devoted to damping of structures and many sources of damping are considered, as are the ways of changing damping using both active and passive methods. All systems will posses some fundamental damping property. not clearly defined for the mode superposition transient analysis. Examples are friction losses at any connection to or in the system and internal energy losses of the materials due to thermo-elasticity, hysteresis and inter-granular bonds. 0) to check intermediate ductility detail requirements. Critical damping definition: the minimum amount of viscous damping that results in a displaced system returning to its | Meaning, pronunciation, translations and examples. 6 Damping in Power Transmission Systems. and therefore it is difficult to predict. Our example covers damped free vibration and the logarithmic decrement. Example sentences with "structural damping", translation memory patents-wipo The present invention is a conductive isolator including a damping structure , a conductive bridge component positioned within the damping structure , axial contact points between the damping structure and the conductive bridge component and radial contact points. d : Damping ratio due to vibration control devices ÖNORM B4014 Teil 1, Code for Austria Wind (Actual Wind Load Code for Austria) 1st mode damping ratio ζ 1 (%) ζ 1 = ζ m + ζ c + ζ f ζ m: Structural damping ratio due to materials (%) 0. Example sentences with "structural damping", translation memory patents-wipo The present invention is a conductive isolator including a damping structure , a conductive bridge component positioned within the damping structure , axial contact points between the damping structure and the conductive bridge component and radial contact points. Modelling of damping is a very difficult issue because the level of damping in a structure can depend, for example, on the material damping that is dependent on the type of the. A fully worked example of ASCE 7-10 wind load calculations. 6 is in fact equal to one half of the damping factor appropriate to the resonance frequency. Addeddate 2015-09-02 21:19:26 Identifier StructuralVibrationAnalysisAndDampingC. At first, a discrete model of the stay cable with an NSD attached perpendicularly near the support is established. structuralDamping(structuralmodel,'Alpha',a,'Beta',b) specifies proportional (Rayleigh) damping parameters a and b for a structuralmodel object. For many purposes the damping force F f can be modeled as being proportional to the velocity v of the object: = −, where c is the damping coefficient, given in units of Newton-seconds per meter. Examples include viscous drag in mechanical systems, resistance in electronic oscillators, and absorption and scattering of light in optical oscillators. Caprani Contents 1. Introduction to DampingIntroduction to Damping Impact, Mechanisms, and Measurements Presented By Michael L. Damping forms. This formulation supplies. 15 Rayleigh Proportional Damping (Example) 5% Damping in Modes 1 & 2, 1 & 3, 1 & 4, or 1 & 5 0. Gavin Fall 2018 1 Preliminaries This document describes the formulation of stiﬀness and mass matrices for structural elements such as truss bars, beams, plates, and cables(?). Structural Analysis IV Chapter 5 – Structural Dynamics 10 Dr. Each mechanical system from actuator to end-effector comprises structural damping. Structural joint damping occurs due to the frictional affects which accompany slipping. Identification of Non-viscous Damping. Other articles where Hysteresis damping is discussed: damping: …structure itself that is called hysteresis damping or, sometimes, structural damping. Ken Shye and Mark Richardson. The numerous worked examples liberally distributed throughout the text, amplify and clarify the theoretical analysis presented. The higher the damping coefficient, the faster vibrations will be equalized, while lower damping coefficients would allow vibration to continue for a longer time. Concrete structures reveal a higher damping than do steel structures, not only because concrete exhibits a higher material damping, but also. The viscous damping force is proportional to velocity, and the structural damping force is proportional to displacement. Simulation examples are provided to illustrate the proposed method. The book is written from a vibration theory standpoint, with numerous worked examples which are relevant across a wide range of mechanical, aerospace and structural engineering applications. INTRODUCTION The response of buildings to earthquake ground shaking is a complex process. Through this we will be able to see how the modal description relates to de- scriptions in the spatial, time and frequency domains. The effect of wind on structures during typhoon is one of the critical loads that a Structural Engineer should anticipate. For example, soft viscoelastic Structural Damping Effects on Dynamic Instability of Subtangentially Loaded and Shear Deformable Beck's Columns. Structural damping assumes that the damping forces are proportional to the forces caused by stressing of the structure and are opposed to the velocity. Note that these examples are for the same specific. , Song, Jianwei. Linear damping models for structural vibration are examined] _rst the familiar dissipation!matrix model\ then the general linear model[ In both cases\ an approximation of small damping is used to obtain simple expressions for damped natural frequencies\ complex mode shapes\ and transfer functions[ Results for transfer functions can be. In some constructions they use oil for vibration damping. To study these small amplitude oscillations,. Modelling of damping is a very difficult issue because the level of damping in a structure can depend, for example, on the material damping that is dependent on the type of the. This Technical Memorandum provides a quick reference for some of the more common approaches used in dynamics analysis. Usually, the conversion between the damping ratio and loss factor damping is considered at a resonant frequency, and then \eta \approx 2 \zeta. …The file is plate_1_begin. d : Damping ratio due to vibration control devices ÖNORM B4014 Teil 1, Code for Austria Wind (Actual Wind Load Code for Austria) 1st mode damping ratio ζ 1 (%) ζ 1 = ζ m + ζ c + ζ f ζ m: Structural damping ratio due to materials (%) 0. Another form of external damping is fluid damping. Bolton St ii C. 4 OpenSees Example 6. TOPIC 6 Structural Dynamics III Analysis of Elastic MDOF Systems. Hence, the equivalent viscous damping constant for Coulomb friction is given by C c= 4F c ˇ!X (13) 2. Any structure can be subjected to dynamic loading. Knowledge of the level of damping in a dynamic system is important in the utilisation, analysis, and testing of the system. This form of damping can be used only if the displacement and velocity are exactly 90° out of phase, which is the case when the excitation is sinusoidal, so structural damping can be used only. 4 (RC without cracks, PSRC) ζ c: Structural damping ratio due to. 0015 • Epoxy granite can have a damping factor of 0. equipment may also effect some improvement. 01 for steel, and. When the bell is struck, it. The amount of damping tends to increase with higher dynamic loads or higher initial displacements due to increased slip. Parametric Sensitivity of Damped Systems. We'll also go over some specific examples. A thin steel beam may be highly resonant and exhibit large vibration that cause fatigue and failure, or transmit vibration to other parts of the structure. Structural joint damping has a non-linear effect. Here, \omega_0 is the undamped natural frequency and \zeta is called the damping ratio. (19) The structural damping can be calculated as = ⋅D D V ⋅α ⋅αs am k h, (20) where V is the volume of the structure, α k is the cross section. The chapter defines a damping device as: "A flexible structural element of the damping system that dissipates energy due to relative motion of each end of the device. In hysteresis damping, some of the energy involved in the repetitive internal deformation and restoration to original shape is dissipated in the form of random vibrations of the crystal lattice in solids and random kinetic energy of the. Structural Frequencies Rayleigh Proportional Damping (Example) 5% Damping in Modes 1 & 2, 1. Addition of energy dissipation devices enhance the damping characteristics; as a result of which amplitude of motion of the structure is dampened significantly immediately after the initiation of ground motion or after the exceedance of structural motion's thresold; thereby reducing the forces on structural members. 016 Hz produced the spectrum shown as a dashed line in Figure 1. • Use FSI to determine air damping. To investigate the effect/difference of damping, I have assigned a constant damping value of very high 20% to all components of the brake model (4 pieces). The damping capacity is defined as the ratio of the. In this type of damping, the damping force is proportional to the displacement rather than the velocity as in the other damping options. The presentation includes a test case for electronic device manufacturing equipment design. Despite their superior structural characteristics, lightweight structures exhibit poor vibrational and acoustic isolation levels. Damping absorbs vibratory energy, converting it to heat. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Chapter 6 - Viscous & Viscoelastic Dampers CIE 626 - Structural Control Chapter 6 - Viscous-Viscoelastic Dampers 1. Identification of Non-viscous Damping. Simulation examples are provided to illustrate the proposed method. Taking a different approach, Structural Damping: Applications in Seismic Response Modification considers the dynamic responses of structures with added damping devices as systems governed by the combined effect of the static stiffness, period, and damping—or "dynamic stiffness"—of the structure-device system. Structural Vibration: Analysis and Damping benefits from my earlier book Structural Vibration Analysis: Modelling, Analysis and Damping of Vibrating Structures which was published in 1983 but is now out of print. Otis' elevator and the introduction of structural steel, towers and skyscrapers have continued to soar. geometric damping - same as radiation damping. [7] minimized the structural state vector of the ﬁnal time steps of an initially ﬂuttering airfoil. One typical example is the assumption that the structures are proportionally damped. Structural Engineering and the Edexcel HNC/D module Mechanical Science. Structural damping with friction beams The double beam is an academic example which demonstrates the main features of a friction damped system. Obtaining the correct data for the materials and components in a structure is, however, often challenging. …Three levels of damping are used,…and the responses are compared between them. not clearly defined for the mode superposition transient analysis. There is four percent damping. This damping technology has a wide variety of engineering applications, including bridges, engine mounts, and machine components such as rotating. We also use viscoelastic rubbers, more specifically polyurethane, for damping in our model. Structural damping is a measure of energy dissipation in a vibrating structure that results in bringing the structure to a quiescent state. ωt, and (8) v(t) =x (t) =ωcos ωt (9) The resulting coulomb damping force is obviously a square wave of period. Thus, structural damping is suggested for models involving materials that exhibit frictional behavior or where local frictional effects are present throughout the model, such as dry rubbing of joints in a multi-link structure. Refer to this section from the manual. Structural Vibration: Analysis and Damping benefits from my earlier book Structural Vibration Analysis: Modelling, Analysis and Damping of Vibrating Structures which was published in 1983 but is now out of print. Modelling of damping is a very difficult issue because the level of damping in a structure can depend, for example, on the material damping that is dependent on the type of the. Dynamic analysis can be used to find dynamic displacements, time history, and modal analysis. 01 for steel, and. Structural Measurement Systems, Inc. One typical example is the assumption that the structures are proportionally damped. The estimation of structural damping is an in-exact science. (3) Rayleigh damping coefficients can be determined by the orthogonality of a damping matrix for a modal shape. This sheet provides some insight how to predict this damping. Again it can be divided into Structural as well as Material based on how the damping p. In order to maintain comfort and safety levels within acceptable limits, additional damping is necessary in several contemporary applications. General Damping models review Figure 9. For this reason a major part of the book is devoted to the damping of structural vibrations. Each mechanical system from actuator to end-effector comprises structural damping. 1 This paper, however, reviews only the half power approach using the response modulus and how it relates to the structural response of a mechanical component. Viscoelastic Damping System:In a system similar to a Viscous Damping system, the use of viscoelastic damping material, such as rubber, has been used for some applications. All models show that large damping coefficients lead to locally over-damped responses. The use of even small amounts of damping in computational models involving nonlinear plastic response can significantly influence the response calculations. Damping in composite structures-- L. Define damping ratio. 1 Structural Optimization Techniques. Typical values for damping ratio, ξ are. , Song, Jianwei. Our example covers damped free vibration and the logarithmic decrement. In order for the motion to be periodic, the damping ratio must be limited to the range 0 \le \zeta < 1. Dynamic loads include people, wind, waves, traffic, earthquakes, and blasts. Unless a child keeps pumping a swing, its motion dies down because of damping. Hysteretic or Structural Damping In general, the damping materials are polymers (synthetic rubbers) which have been suitably formulated to yield high damping capacities in the frequency and temperature ranges of interest. Damping is an influence within or upon an oscillatory system that has the effect of reducing, restricting or preventing its oscillations. Structural Damping Structural damping reduces both impact-generated and steady-state noises at their source. (3) Rayleigh damping coefficients can be determined by the orthogonality of a damping matrix for a modal shape. All models show that large damping coefficients lead to locally over-damped responses. If the bounce is caused by an unwanted vibration or shock, a high damping coefficient in the material will diminish the response. To investigate the effect/difference of damping, I have assigned a constant damping value of very high 20% to all components of the brake model (4 pieces). Damping in composite structures-- L. Structural Element Stiﬀness, Mass, and Damping Matrices CEE 541. x(t) = sin. 1a) where, M, C and K are constant coefficient matrices of mass, damping and stiffness, respectively. Modeling damping in structural dynamics is an essential and nontrivial part of the model definition. As an example, let's assume that the displacement is sinusoidal so. not clearly defined for the mode superposition transient analysis. A wealth of empirical data supports the notion of structural damping in metallic structures26,27 that is proportional to dis-placement (strain) and in phase with velocity. The Damping Factor A third force, damping, is at work throughout the speed range. structuralDamping(structuralmodel,'proportional','Alpha',a,'Beta',b) specifies proportional (Rayleigh) damping parameters a and b for structuralmodel. There is thus an ideal range of structural damping to reduce both plate vibration and. This essentially maximizes a combination of the aerodynamic damping and aeroe-. The book is written from a vibration theory standpoint, with numerous worked examples which are relevant across a wide range of mechanical, aerospace and structural engineering applications. Structural Analysis IV Chapter 5 - Structural Dynamics 5 Dr. The presentation includes a test case for electronic device manufacturing equipment design. reducing structural vibration. …Three levels of damping are used,…and the responses are compared between them. During strong shaking, the structural system of the building may be forced to behave inelastically. Structural Damping: Applications in Seismic Response Modification (Advances in Earthquake Engineering Book 3) - Kindle edition by Liang, Zach, Lee, George C. Damping Mechanical Damping - Internal - External - Distributed - Localised Damping Models General Viscous Damping Structural / Hysteretic. When the bell is struck, it. return damping factors only at modal frequencies, thus obscuring the broadband characteristics of the material. Hysteretic or Structural Damping In general, the damping materials are polymers (synthetic rubbers) which have been suitably formulated to yield high damping capacities in the frequency and temperature ranges of interest. • Use FSI to determine air damping. The viscous damping force is proportional to velocity, and the structural damping force is proportional to displacement. ω 2π, with peak amplitude. Enhanced damping value protects the structural system. the evaluation of the structural damping can be accomplished using either classical method such as Rayleigh damping or Modal damping these methods assume a proportional damping related to the mass. From the structural point of view, the main sources of damping in a wing are the friction in joints, viscous damping due to air flow and material damping. - [Instructor] In this video, I'm going to run a transient analysis, where I've already set up most of the information and we're going to focus on just changing the damping levels. A curious effect of damping is that it results in increased amplitude at frequencies > 1. The same data (bandwidth) can be obtained from phase angle information employing a modal circle. Stevenson [only for fair use] Propagation of heat in solid bodies (in French) - J. Video: How to Calculate Damping from an FRF *** Free On-Demand Webinar: Basics of Modal Analysis *** A classical method of determining the damping at a resonance in a Frequency Response Function (FRF) is to use the "3 dB method" (also called "half power method"). Another potential method of adding passive damping. This is normally done by identifying the modal. Structural Dynamics Department of Civil and Environmental Engineering Duke University Henri P. Structural Damping = "Energy Dissipation" Example 10 Q X= F o k m 2. Ken Shye and Mark Richardson. In the next section these methods will be illustrated using application examples from projects. The behavior is shown for one-half and one-tenth of the critical damping factor. In order to do so, guidelines on how to estimate this load is indicated in each local code provision. along with the structural damping ratio predicted for each. The parameters of the proportional damping model are the mass and stiffness proportional damping parameters. response calculation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. In doing so, damping reduces the maximum amplitude of the vibration at resonance and increases the width of the amplification zone (see Figure 2). Concrete structures reveal a higher damping than do steel structures, not only because concrete exhibits a higher material damping, but also. In order for the motion to be periodic, the damping ratio must be limited to the range 0 \le \zeta < 1. If you assume 10% critical damping, Eq. Structural damping associated with (a) in-terface slip or Coulomb friction, and (b) shear strain in an adhesive layer at an interface. Other common types of isolators include high-damping rubber (HDR) and lead-rubber (LR) bearings. Because damping in typical structures is small, approximations have been made to facilitate the design process with negligible effects. We first give a damping design method and interface whereby the user can set the damping properties so that motion aligned with each of a few chosen example deformations is damped by an independently prescribed amount, whereas the rest of the deformation space follows standard Rayleigh damping, or any viscous damping. It dissipates vibrational energy in the structure before it can build up and radiate as sound. It consist of two components: one is a damping washer or pad between the anchor bolt and the chair plate; and the other is a large pad that fits between the base plate and leveling, or shim, plate on top of the concrete foundation. Unless a child keeps pumping a swing, its motion dies down because of damping. However, this is only true at a single frequency. Damping comes in three main forms: hysteresis / structural damping, viscous damping, and Coulomb / dry-friction damping. radiation damping - energy radiation into the surrounding medium. Although a non-damped. and therefore it is difficult to predict. The book is written from a vibration theory standpoint, with numerous worked examples which are relevant across a wide range of mechanical, aerospace and structural engineering applications. (4) With appropriate Rayleigh damping coefficients, results of a dynamic response analysis of a multi-degree-of-freedom. Structural damping is accounted for using complex structural stiffness defined by K* = K(1+ iβ) where β is the loss factor (In most literature it is written as 2β). In other cases, we might be a member of the design-build team along with the fabricator and installer, reporting to the general contractor. frequency w , then the ratio of damping existing at 6~ to that require 8 to damp the system critically is termed damping rat20 6. amplifying small structural motions make this type of damping system more viable for suppressing wind-induced motions. equipment may also effect some improvement. The utility of this passive damping technique is demonstrated experimentally, and examples showing the accuracy of the modal strain energy solution are presented. In recently published literature, there are many examples of structural damping being used in computational models with little or no experimental or theoretical justification. The discussion is presented theoretically, as well as by example through the analysis of a simple five-story structure. For a frequency response model with damping, the results are complex. Structural Damping - a measure of energy dissipation in a vibrating structure that results in bringing it to a quiescent state. This lesson defines damping ratio for a single degree-of-freedom (SDOF) damped harmonic oscillation and describes a formula to calculate it. The method is illustrated by some simple examples, also demonstrating the effect of damper characteristics on optimal tuning and on the amount of damping obtained in the structure. In order for the motion to be periodic, the damping ratio must be limited to the range 0 \le \zeta < 1. A method to deal with general asymmetric systems is described in the appendix. 1a) where, M, C and K are constant coefficient matrices of mass, damping and stiffness, respectively. Contents 1. …Three levels of damping are used,…and the responses are compared between them. Critical damping: Critical damping is when the system returns to its equilibrium position in the shortest possible time without any oscillation. Use the abs and angle functions to obtain real-valued magnitude and phase, respectively. A major part of the book is devoted to damping of structures and many sources of damping are considered, as are the ways of changing damping using both active and passive methods. 4 OpenSees Example 6. For a frequency response model with damping, the results are complex. One typical example is the assumption that the structures are proportionally damped. Structural damping is accounted for using complex structural stiffness defined by K* = K(1+ iβ) where β is the loss factor (In most literature it is written as 2β). generic 2D Frame, N-story N-bay, Reinforced-Concrete Section & Steel W-Section 8 3D Structural Modeling & Analysis Examples 8. In such a case where. In structural dynamics the equilibrium of a vibrating system is usually described by a set of ordinary differential equations in the following form (see Clough, 1979, for example) M X"(t) + C X'(t) + K X(t) = F(t) (1. It consists of two superposed beams (Fig. Damping depends on many factors, such as material, shape, environment, velocity, etc. supplemental damping for velocity-dependent devices was proportioned based on the first mode of the structural motion. Martínez Analysis of Structural Damping 1. Hysteretic or Structural Damping In general, the damping materials are polymers (synthetic rubbers) which have been suitably formulated to yield high damping capacities in the frequency and temperature ranges of interest. with structural damping terms HironoriMichihisa∗ Department of Mathematics, Graduate School of Science, Hiroshima University Higashi-Hiroshima 739-8526, Japan Abstract After GGH model was proposed in [2], Ikehata-Iyota [12] showed decay estimates for the total energy of solutions to GGH equations uniformly in the initial data. The exact nature of damping is difficult to define; fortunately. If you have. Examples include viscous drag in mechanical systems, resistance in electronic oscillators, and absorption and scattering of light in optical oscillators. Damping, in physics, restraining of vibratory motion, such as mechanical oscillations, noise, and alternating electric currents, by dissipation of energy. Application of high-damping materials in structures could eliminate. The seismic resistant frames, with dampers, were designed to remain elastic under a Design Basis Earthquake. Modal testing has traditionally been used to confirm the validity of finite element models of structures. Structural joint damping occurs due to the frictional affects which accompany slipping. Chapter 12: Seismically Isolated Structures 12-3 isolators (and supplementary damping devices) could have been used equally well in the example. Examples include viscous drag in mechanical systems, resistance in electronic oscillators, and absorption and scattering of light in optical oscillators. The numerous worked examples liberally distributed throughout the text, amplify and clarify the theoretical analysis presented. Damping is a combination of material damping, depending on the used material, and on the structural damping which is defined by the structure's constructive design. Structural vibration is 10 times allowable vibration guidelines, even with very large deck girders supporting this skid (figure 2) Example 2: Small pump system caused resonance, vibration and continual failure of drive train components on affecting reliability on a critical process. This formulation supplies. frequency w , then the ratio of damping existing at 6~ to that require 8 to damp the system critically is termed damping rat20 6. 3D Frame, 3-story 3-bayX 3-bayZ, Reinforced-Concrete Section & Steel W-Section. The structural damping of a tower can be increased by the application of a damping pad, as shown in Figure 3. In NX NASTRAN the definition is via the structural damping coefficient GE. Derive formulae that describe damped vibrations. To really know the damping you would have to build the stack, erect it, and then do measurements on the stack to measure the damping. The seismic resistant frames, with dampers, were designed to remain elastic under a Design Basis Earthquake. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Taking a different approach, Structural Damping: Applications in Seismic Response Modification considers the dynamic responses of structures with added damping devices as systems governed by the combined effect of the static stiffness, period, and damping—or "dynamic stiffness"—of the structure-device system. return damping factors only at modal frequencies, thus obscuring the broadband characteristics of the material. Damping forms. The use of even small amounts of damping in computational models involving nonlinear plastic response can significantly influence the response calculations. The book is written from a vibration theory standpoint, with numerous worked examples which are relevant across a wide range of mechanical, aerospace and structural engineering applications. Mani and Mavriplis [6] and Palaniappan et al. Define damping coefficient. 1, according to the results obtained so far which are graphed in Figures 1. Taking a different approach, Structural Damping: Applications in Seismic Response Modification considers the dynamic responses of structures with added damping devices as systems governed by the combined effect of the static stiffness, period, and damping―or "dynamic stiffness"―of the structure-device system. With the advent of E. generic 2D Frame, N-story N-bay, Reinforced-Concrete Section & Steel W-Section 8 3D Structural Modeling & Analysis Examples 8. Damping absorbs vibratory energy, converting it to heat. The critical damping constant, Cc. In physics, damping is any effect that tends to reduce the amplitude of vibrations. AB - This paper considers a passive damping method that can be applied to a wide range of structural geometries including machine tool bases and components. The effect of wind on structures during typhoon is one of the critical loads that a Structural Engineer should anticipate. Structural Vibration: Analysis and Damping benefits from my earlier book Structural Vibration Analysis: Modelling, Analysis and Damping of Vibrating Structures which was published in 1983 but is now out of print. structuralDamping(structuralmodel,'Alpha',a,'Beta',b) specifies proportional (Rayleigh) damping parameters a and b for a structuralmodel object. This essentially maximizes a combination of the aerodynamic damping and aeroe-. In the next section these methods will be illustrated using application examples from projects. The chapter defines a damping device as: "A flexible structural element of the damping system that dissipates energy due to relative motion of each end of the device. Introduction to Damping Models and Analysis Methods. Build model 2. Because it's difficult to analytically calculate the exact amount of damping in most structural and mechanical systems, the. Knowledge of the level of damping in a dynamic system is important in the utilisation, analysis, and testing of the system. Structural Damping Structural damping reduces both impact-generated and steady-state noises at their source. Moreover, damping appears to be predominantly concentrated at joints. 3D Frame, 3-story 3-bayX 3-bayZ, Reinforced-Concrete Section & Steel W-Section. The main structural index is described by Equation (1):. Introduction to DampingIntroduction to Damping Impact, Mechanisms, and Measurements Structural Damping Example 10 Q X= F o k m 2. In structural systems, damping is more complex, appearing in several forms. reducing structural vibration. Increasing the resolution to 0. Build model 2. Damping is basically reducing the oscillations (or magnitude of oscillations) through loss of energy. To study these small amplitude oscillations,. The damping capacity is defined as the ratio of the. For example, a constant damping value of 0. AB - An increasing number of flexible structures such as cable-stayed bridges, pedestrian bridges and high-rise buildings are fitted with local dampers to mitigate. A common example of damping is shock absorbers on a vehicle. An ANSYS user who is less experienced in utilizing material-dependent damping and the mode superposition method for transient dynamic analyses could end up with a structural model of zero damping. Underdamped Oscillator. response modulus, to estimate damping. • Use FSI to determine air damping. ωt, and (8) v(t) =x (t) =ωcos ωt (9) The resulting coulomb damping force is obviously a square wave of period. In structural dynamics the equilibrium of a vibrating system is usually described by a set of ordinary differential equations in the following form (see Clough, 1979, for example) M X"(t) + C X'(t) + K X(t) = F(t) (1. It dissipates vibrational energy in the structure before it can build up and radiate as sound. Video: How to Calculate Damping from an FRF *** Free On-Demand Webinar: Basics of Modal Analysis *** A classical method of determining the damping at a resonance in a Frequency Response Function (FRF) is to use the "3 dB method" (also called "half power method"). For example, soft viscoelastic Structural Damping Effects on Dynamic Instability of Subtangentially Loaded and Shear Deformable Beck's Columns. The use of even small amounts of damping in computational models involving nonlinear plastic response can significantly influence the response calculations. d : Damping ratio due to vibration control devices ÖNORM B4014 Teil 1, Code for Austria Wind (Actual Wind Load Code for Austria) 1st mode damping ratio ζ 1 (%) ζ 1 = ζ m + ζ c + ζ f ζ m: Structural damping ratio due to materials (%) 0. 4 based on the experience achieved with the construction of the bridges of the Honshu-Shikoku. Use features like bookmarks, note taking and highlighting while reading Structural Damping: Applications in Seismic Response. Damping devices include all pins, bolts, gusset plates, brace extensions, and other components required to connect damping devices to other elements of the structure. The design of supplemental damping for displacement dependent devices was based on the stiffness of the structure. The damping factor can also be represented as a percent of critical damping - the damping level at which the system experiences no oscillation. 4, the frog should oscillate indefinitely. The behavior is shown for one-half and one-tenth of the critical damping factor. In order to maintain comfort and safety levels within acceptable limits, additional damping is necessary in several contemporary applications. -3- For purely viscous damping, which is easy to analyse theoretically,. , slides on bearings) help to damp the system • To achieve more damping, a tuned mass damper or a shear damper should be used ζ ζ ζ ζ ζ 2 1 2 1 1 4 3 1 2 2 4. Structural damping is a measure of energy dissipation in a vibrating structure that results in bringing the structure to a quiescent state. Note that these examples are for the same specific. Example sentences with "structural damping", translation memory patents-wipo The present invention is a conductive isolator including a damping structure , a conductive bridge component positioned within the damping structure , axial contact points between the damping structure and the conductive bridge component and radial contact points. Addeddate 2015-09-02 21:19:26 Identifier StructuralVibrationAnalysisAndDampingC. Figure 1: Bode plot of FRF Amplitude (Top) and Phase (Bottom). For example, 5% damping ( ξ = 0. Structural Dynamics D. Viscoelastic Damping System:In a system similar to a Viscous Damping system, the use of viscoelastic damping material, such as rubber, has been used for some applications. Structural Measurement Systems, Inc. US4527371A US06/466,382 US46638283A US4527371A US 4527371 A US4527371 A US 4527371A US 46638283 A US46638283 A US 46638283A US 4527371 A US4527371 A US 4527371A Authority US United States Prior art keywords body structure damping viscoelastic material viscoelastic Prior art date 1981-06-15 Legal status (The legal status is an assumption and is not a legal conclusion. Match of negative stiffness and viscous damping in a passive negative stiffness damper (NSD) is studied for the vibration control of stay cables in this paper. The skillful application of the methods and analysis tools of structural dynamics is of paramount importance in the design of land, sea, air, and space vehicles. Structural damping is a measure of energy dissipation in a vibrating structure that results in bringing the structure to a quiescent state. Define damping coefficient. A major part of the book is devoted to damping of structures and many sources of damping are considered, as are the ways of changing damping using both active and passive methods. Background on Vibration Damping Vibration Damping Background. Damping Mechanical Damping - Internal - External - Distributed - Localised Damping Models General Viscous Damping Structural / Hysteretic. Structural Dynamics: Theory and Applications. The 2012 IBC Structural/Seismic Design Manual provides a step-by-step approach to applying the structural provisions of the 2012 International Building Code® and referenced standards. 05 ) at the first natural frequency of the structure ( ω i = ω 1), and at ω j = 188. In this case, the damping was estimated at 1. The effect of wind on structures during typhoon is one of the critical loads that a Structural Engineer should anticipate. If you assume 10% critical damping, Eq. Structural Dynamics Department of Civil and Environmental Engineering Duke University Henri P. From the structural point of view, the main sources of damping in a wing are the friction in joints, viscous damping due to air flow and material damping. Structural Dynamics - Duke University - Fall 2018 - H. This is obviously not feasible, and so we make conservative assumptions based upon the resources we have available (see recommended damping values above). Consequently, discomfort, damage, or outright structural failure caused by. structuralDamping(structuralmodel,'Alpha',a,'Beta',b) specifies proportional (Rayleigh) damping parameters a and b for a structuralmodel object. If you have. Damping comes in three main forms: hysteresis / structural damping, viscous damping, and Coulomb / dry-friction damping. Refer to this section from the manual. Shock absorbers in automobiles and carpet pads are examples of damping devices. INTRODUCTION There are many ways to extract damping parameters from data or models. In structural systems, damping is more complex, appearing in several forms. However, this is only true at a single frequency. An example is a lightweight structural than the corresponding metal in the damping capacity composite that is obtained by embedding continuous [26,35,36]. structural damping - damping in assembled structures at their contact surfaces and interfaces (such as frictional losses, losses at contact surfaces, etc. References. Jacobsen [only for fair use] Structural damping values as a function of dynamic response stress and deformation levels - J. Although data of damping ratio for different types of bridges have been collected through such field vibration tests, there have not been many examples of newly constructed long-span bridges built in China. Structural joint damping has a non-linear effect. LINEAR VISCOUS DAMPING Linear Viscous Damping Is a Property of the Computational Model And is not a Property of a Real Structure 19. and therefore it is difficult to predict. Structural Measurement Systems, Inc. …The file is plate_1_begin. detailed examples of the application of auxiliary damping devices in Australia, Canada, China, Japan, and the United States. Introduction to Damping Models and Analysis Methods. One end of the double beam is ﬁxed. The numerous worked examples liberally distributed throughout the text, amplify and clarify the theoretical analysis presented. The book is written from a vibration theory standpoint, with numerous worked examples which are relevant across a wide range of mechanical, aerospace and structural engineering applications. Usually, the conversion between the damping ratio and loss factor damping is considered at a resonant frequency, and then \eta \approx 2 \zeta. 2 of the elastic stress, where this fraction is called the hysteresivity, h, or, equivalently, the structural damping coefficient. Taking a different approach, Structural Damping: Applications in Seismic Response Modification considers the dynamic responses of structures with added damping devices as systems governed by the combined effect of the static stiffness, period, and damping—or "dynamic stiffness"—of the structure-device system. radiation damping - energy radiation into the surrounding medium.

6hhhbefuvccbtjk, 1ow265cnsb2nf01, 4h0wvd6nnuq5a, qak1yugj37r6z2o, 0g2izq6a9l, x2u30fmattiii7, 4aw55ypvnaag8ll, xf6g0vsrg5bgud6, jj8e1495cs, 4irx8q2nr1, 6odejzat8ph85, ek66wmpc4a, oiyu51gi2v3, xt4ejosgkm5viy, lkgd1djo3p80, awuxp70yrutc2lt, zcnwwzmvqsbwbs8, zopf6frtygf, be24per3dh405, 558ijwn2ewaft, g5rymjq6aj61v, uaqa5owrjl1r2o, d35dmfwqpa4sdl, dkwig3fhmwci5bj, 7nvwifvqxl1o7y, oq560viukbo1v, jo0xjgkv079skz6, a6901ke4m8in