Equivalent damping for displacementbased seismic design. Rayleigh damping does afford certain mathematical conveniences and is widely used to model internal structural damping. The simulation results of simscale were compared to the results presented in case a and case b of sdls123. For example, one can think of the first harmonic damping to half its magnitude in 10 seconds, whereas the second mode might damp to half its magnitude in 2 seconds. Pdf computation of rayleigh damping coefficients for. Damping faq technical knowledge base computers and. To define rayleigh damping, you specify two rayleigh damping factors. It is also called the halfpower point, or 3db point damping. Computation of rayleigh damping coefficients for large systems. Freque explic f2 f1 0 specifies the explicit frequencies f1 and f2 used for calculating the rayleigh damping coefficients. Calculating rayleigh damping parameters posted nov 4, 2010, 12. Furthermore, the assumed displacement function introduces additional constraints which increase the stiffness of the system. Damping ratio is a very important parameter for building structures in the analysis of dynamic response. This is because the rayleigh damping tends to work against the feeding and can cause the simulation to become unstable.
Alpha and beta are constants used to set the amount of damping. Rayleigh damping rayleigh damping matrix c can be represented as the linear combination of the mass matrix m and the stiffness matrix k. For a quantitative measure of damping the halfpower bandwidth method can be employed. Compensation is exact if modal damping hypothesis 6 is veri. It is also assumed that viscous damping can be modeled using a linear viscous damping term. Damping, a property of the material and the structure, influences dynamic response. The eigenvalue problem for a general system of the form.
In our new model, the stiffness proportional dampin g is replaced. Computation of rayleigh damping coefficients for the. Evaluation of the rayleigh damping model for buildings. This is partly due to the scarcity of quality damping data for higher modes, but given the lack of thorough evaluation it appears like it has been given for granted that the rayleigh damping is an adequate model for representing damping in buildings responding elastically. Modelling damping in linear dynamic systems final bachelor project dct report number. Initialstiffness damping generally leads to faster convergence during analysis, but may overestimate damping and hence be unconservative. Each line type and turbine has structural damping properties determined by a named rayleigh damping coefficient data set. It is recommended for lm runs with ifs frames, but it can be used even if the boundary conditions are defined on a full grid. For a nonconservative force the net work won a closed path is nonzero. Problems with rayleigh damping in baseisolated buildings. Based on the above discussion, it is easy to also think of each mode damping independently. Explicit algorithm for collapse simulation comparison of computational speed algorithm damping model cost of each step explicitleapfrog mass damping 0.
The xaxis is time, and the yaxis is a nodal displacement. Determination of rayleigh damping coefficient for natural. In this paper, finite element modal analysis is used on square natural damping rubber plate with various boundary conditions to determine its dynamic properties and damping coefficients. Rayleigh damping is a combina tion of mass proportional damping and stiffness proportional dampin g, as illustrated in figure 12.
Off suppresses the calculation of rayleigh damping coefficients. After the definition of rayleigh damping, we propose a rheological interpretation of rayleigh damping. To compute the rayleigh damping coefficients, 210% damping to the critical damping has been assumed for this analytical study. In this paper a more general expression of the damping matrix is proposed while retaining the advantage of classical normal modes. Rayleigh damping can also be used in directsolution steadystate dynamic analyses and subspacebased steadystate dynamic analyses to get quantitatively accurate results, especially near natural frequencies. For the analysis, an feabased software ansys is utilized.
Effective damping value of piezoelectric transducer. The rayleigh s quotient represents a quick method to estimate the natural frequency of a multidegreeoffreedom vibration system, in which the mass and the stiffness matrices are known. The extended forms provide more choices in formulating a damping matrix. As such, rayleigh damping models can provide a clear physical meaning and present a. Equivalent damping for displacementbased seismic design of pilesupported wharves with soilpile interaction. In the ansys software, only a value of each a di and b di can be input in a load step, regardless of the frequencies that are active in that load step. Damping coefficients technical knowledge base computers and. Gavin a rayleigh damping matrix is proportional to the mass and sti. Rayleigh damping is the main form in direct integral method for structural nonlinear dynamic analysis under seismic wave. As shown here, even when used as recommended for combining subsystems with disparate damping properties, rayleigh damping results in undesirable suppression of the first mode response. If you get into a nonlinear dynamic problem, youll see that the only damping formulation available is the rayleigh, so you are forced to use that in nl studies.
An overview of the tunedmass damper and guidelines for modeling the device. If modaldirect is selected the user can specify the viscous damping factor for each mode separately. The rayleighs quotient represents a quick method to estimate the natural frequency of a multidegreeoffreedom vibration system, in which the mass and the stiffness matrices are known. Pdf initial versus tangentstiffness based rayleigh damping in.
If all the modal damping ratios are defined as the same, as to the dynamic analysis for that structure, the results of analysis will be inappropriate. Hi guys i have a problem with constant modal damping in sap2000. The aim of this test case is to validate the following functions. Storyadding rc structure of lightweight steel is composed by two different material stories.
It considers a massproportional and a stiffnessproportional damping in order to achive the real damping lets say 5%. Rayleigh s method requires an assumed displacement function. An extended rayleigh damping matrix, called caughey damping 1,2, can be computed from c m jxn 2 jn 1. Equation 2 you can define rayleigh damping for linear and nonlinear dynamic studies. The generalized proportional damping expresses the damping matrix in terms of any nonlinear function involving specially arranged mass and stiffness matrices so that the system still posses classical normal modes. Thus, rayleigh s method yields an upper limit of the true fundamental frequency.
Rayleighs quotient in vibrations analysis wikipedia. Pdf computation of rayleigh damping coefficients for large. Within all load cases of a certain type, damping is applied consistently, though additional damping may be added to individual load cases. Development and application of explicit methods in. Rayleigh damping is not applied to any line segment whose unstretched length is actively varying because of line feeding. By applying the modal coordinate transformation, the modal damping matrix c becomes diagonal. This enables one to model practically any type of variations in the modal damping. Learn about the sap2000 structural analysis and design program. Influence of mode dependent rayleigh damping on transient. This outcome could be used for investigations of noise, harshness and fatigue. The method thus reduces the dynamic system to a singledegreeoffreedom system. There are two optional, mutually exclusive parameters. The slide shows a physical interpretation for rayleigh damping.
Rayleigh damping is characterized by the two constants a and b, whereas the damping coefficient of the concrete is 0. Rayleigh damping is an empirical means by which to damp all frequencies. Using modal damping for full model transient analysis. The damping behavior of damped system is dependent on numerical values of eq. Rayleigh damping has been originally proposed and is suitable for single degree of freedom systems. Fedem, structural damping, rayleigh damping, frf, dynamic. Rayleigh damping in abaqusexplicit dynamic analysis. Sap2000 allows users to either specify coefficients. A certain type of damping is available for each type of load case. Rayleighs method requires an assumed displacement function. Suitability for an incremental approach to numerical solution merits its use. Finite element steadystate vibration analysis considering. The rayleigh dissipation function, as we will see, will allow us to describe the nonconservative force of friction, hence well focus on nonconservative forces in this report. Modal damping is used for responsespectrum and modal.
Limited by the stable time increment, the stiffness proportional damping is usually neglected in abaqusexplicit, and only a simplified mass proportional damping is used, which can be derived from the fundamental frequency and the critical damping factor. Multiple such data sets can be defined, each with the following data. The sap name has been synonymous with stateoftheart analytical methods since its introduction over 30 years ago. A series of finite element fe time history and steadystate analyses using sap2000 have been performed to examine the effects of. The objective of this paper is to present a study on the formulation of rayleigh damping for a damped linear mechanical system. In that case, rayleigh damping should be compensated in order to obtain desired modal damping ratios. Determination of the rayleigh damping coefficients of.
Formulation of rayleigh damping and its extensions. Modal damping vs rayleigh damping solidworks forums. As such, rayleigh damping models can provide a clear physical meaning and present a convenient expression. Computation of rayleigh damping coefficients for large systems article pdf available in electronic journal of geotechnical engineering 43. To approximate modal damping in terms of hysteretic damping, d m can be set to zero and d k can be calculated using the relation d k. For instance, a rayleigh damping model is widely used because of its excellent advantages 10. It doesnt seem to have an effect on the response when i change the damping, even if i set it t modal damping in sap2000 computers and structures. Study on rayleigh damping in dynamic analysis for story. Jun 22, 2014 damping, a property of the material and the structure, influences dynamic response. Damping technical knowledge base computers and structures. It can be safely assumed, at least in earths atmosphere, that the dominant damping mechanism for most structures is the viscous damping of the surrounding air. Considering the resonance frequency expression w km the critical damping. During nonlinear time history analyses, the rayleigh damping was used to represent elastic damping. This form of c is orthogonal with respect to the system eigenvectors.
Ahmad, damping is important whenever you are interested in the transient response of your structure. Structural software for analysis and design sap2000. During formulation, the damping matrix is assumed to be proportional to the mass and stiffness matrices as follows. Abstract damping is an important issue in modelling dynamic systems.
The consideration of rayleigh damping coefficients of. Mass and stiffnessproportional damping, normally referred to as rayleigh damping, is commonly used in nonlineardynamic analysis. Determination of the rayleigh damping coefficients of steel. In the nonlinear timehistory analysis for highrise building, different damping models may lead to results with great difference. Computation of rayleigh damping coefficients for the seismic. Rayleigh damping came out of linear theory massspringdashpot systems where it is easy to view each mode independently. Damping is a function of velocity, so if there is no motion then there will be no damping. Rayleigh damping rayleigh damping is a classical method to build easily the damping matrix c of a numerical model 5,7 under the following form. Straight beam with damping of rayleigh simscale documentation.
At least one study has indicated that when used improperly, superstructure rayleigh damping leads to excessive damping of the response of a baseisolated structure. By means of examining the existing theory on rayleigh damping, extensions of rayleigh damping are proposed in terms of a double series. Sap2000 follows in the same tradition featuring a very sophisticated, intuitive and versatile user interface powered by an unmatched analysis engine and design tools for engineers working on transportation, industrial, public works, sports, and other facilities. The damping ratio is related to the rayleigh damping coefficients by 26. As far as the stiffness proportional part of rayleigh damping is concerned, either the initial structural stiffness or the. Classical damping, nonclassical damping and complex modes.
For example, if a constant 5% modal damping is used for all modes, the equivalent hysteretic damping value is a constant d k. In fact, setting the rayleigh damping to be both mass and stiffness proportional, as usually done in structural engineering practice, leads to a severe underestimation of the hysteretic damping of the soil, as shown in the example of fig. Equivalent damping for displacementbased seismic design of. Obtained responses show that there is considerable effect of mode dependent damping on response of the system. The type of damping described by equation 1 is known as rayleigh or proportional damping. Analysis of safetyrelated nuclear structures and commentary, asce 498 standard, 2000. For hinges modeled as links, the stiffnessproportional damping used for directintegration timehistory analyses may now be specified by the user to be proportional to the initial stiffness of the hinge the current behavior, the tangent stiffness, or a mixture of the two. Any excitation in the time domain will be followed by a decayed amplitude of response as energy is converted in the system. The level of damping can be subjectively determined by noting the sharpness of resonant peak at f 1 figure 3.
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