The damping ratio is related to the rayleigh damping coefficients by 26. Thus, rayleigh s method yields an upper limit of the true fundamental frequency. Study on rayleigh damping in dynamic analysis for story. Calculating rayleigh damping parameters posted nov 4, 2010, 12. If modaldirect is selected the user can specify the viscous damping factor for each mode separately. 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. The eigenvalue problem for a general system of the form.
During formulation, the damping matrix is assumed to be proportional to the mass and stiffness matrices as follows. The method thus reduces the dynamic system to a singledegreeoffreedom system. Mass and stiffnessproportional damping, normally referred to as rayleigh damping, is commonly used in nonlineardynamic analysis. Computation of rayleigh damping coefficients for large systems article pdf available in electronic journal of geotechnical engineering 43. Hi guys i have a problem with constant modal damping in sap2000. The extended forms provide more choices in formulating a damping matrix. To define rayleigh damping, you specify two rayleigh damping factors. Any excitation in the time domain will be followed by a decayed amplitude of response as energy is converted in the system. By means of examining the existing theory on rayleigh damping, extensions of rayleigh damping are proposed in terms of a double series. After the definition of rayleigh damping, we propose a rheological interpretation of rayleigh damping. 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. Damping, a property of the material and the structure, influences dynamic response. Thus, rayleighs method yields an upper limit of the true fundamental frequency. Based on the above discussion, it is easy to also think of each mode damping independently. Rayleigh damping came out of linear theory massspringdashpot systems where it is easy to view each mode independently. It is also called the halfpower point, or 3db point damping. 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. The objective of this paper is to present a study on the formulation of rayleigh damping for a damped linear mechanical system. Modes number m2 m1 0 specifies that the frequecies used for calculating the rayleigh damping coefficients are the eigenfrequencies of modes m1 and m2. This form of c is orthogonal with respect to the system eigenvectors. Using modal damping for full model transient analysis. The damping behavior of damped system is dependent on numerical values of eq. For the analysis, an feabased software ansys is utilized.
Damping is a function of velocity, so if there is no motion then there will be no damping. Damping faq technical knowledge base computers and. Structural software for analysis and design sap2000. To compute the rayleigh damping coefficients, 210% damping to the critical damping has been assumed for this analytical study. For example, if a constant 5% modal damping is used for all modes, the equivalent hysteretic damping value is a constant d k. Rayleighs quotient in vibrations analysis wikipedia. There is a very limited number of studies on damping of higher modes. The xaxis is time, and the yaxis is a nodal displacement. 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. Problems with rayleigh damping in baseisolated buildings. Suitability for an incremental approach to numerical solution merits its use. This enables one to model practically any type of variations in the modal damping. 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.
Classical damping, nonclassical damping and complex modes. Computation of rayleigh damping coefficients for the. Rayleigh damping is characterized by the two constants a and b, whereas the damping coefficient of the concrete is 0. A certain type of damping is available for each type of load case. Furthermore, the assumed displacement function introduces additional constraints which increase the stiffness of the system. Storyadding rc structure of lightweight steel is composed by two different material stories. In this paper a more general expression of the damping matrix is proposed while retaining the advantage of classical normal modes. By applying the modal coordinate transformation, the modal damping matrix c becomes diagonal. Equivalent damping for displacementbased seismic design.
For a quantitative measure of damping the halfpower bandwidth method can be employed. Rayleigh damping does afford certain mathematical conveniences and is widely used to model internal structural damping. A series of finite element fe time history and steadystate analyses using sap2000 have been performed to examine the effects of. Rayleigh damping is the main form in direct integral method for structural nonlinear dynamic analysis under seismic wave. The slide shows a physical interpretation for rayleigh damping. Off suppresses the calculation of rayleigh damping coefficients. Influence of mode dependent rayleigh damping on transient.
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. Determination of rayleigh damping coefficient for natural. Determination of the rayleigh damping coefficients of. 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. Explicit algorithm for collapse simulation comparison of computational speed algorithm damping model cost of each step explicitleapfrog mass damping 0. This outcome could be used for investigations of noise, harshness and fatigue. This is because the rayleigh damping tends to work against the feeding and can cause the simulation to become unstable. Fedem, structural damping, rayleigh damping, frf, dynamic. 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. The type of damping described by equation 1 is known as rayleigh or proportional damping. Formulation of rayleigh damping and its extensions. As such, rayleigh damping models can provide a clear physical meaning and present a convenient expression. Alpha and beta are constants used to set the amount of damping.
Rayleigh damping is an empirical means by which to damp all frequencies. Computation of rayleigh damping coefficients for the seismic. The aim of this test case is to validate the following functions. As such, rayleigh damping models can provide a clear physical meaning and present a. Each line type and turbine has structural damping properties determined by a named rayleigh damping coefficient data set. An overview of the tunedmass damper and guidelines for modeling the device. Damping coefficients technical knowledge base computers and. In the nonlinear timehistory analysis for highrise building, different damping models may lead to results with great difference. During nonlinear time history analyses, the rayleigh damping was used to represent elastic damping. This paper proposes several stateoftheart methods for evaluating effective soil damping that could be modelled in fe finite element software i. Finite element steadystate vibration analysis considering. The consideration of rayleigh damping coefficients of.
Evaluation of the rayleigh damping model for buildings. In our new model, the stiffness proportional dampin g is replaced. There are two optional, mutually exclusive parameters. Pdf initial versus tangentstiffness based rayleigh damping in. Analysis of safetyrelated nuclear structures and commentary, asce 498 standard, 2000. 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. Effective damping value of piezoelectric transducer. The sap name has been synonymous with stateoftheart analytical methods since its introduction over 30 years ago. 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. As far as the stiffness proportional part of rayleigh damping is concerned, either the initial structural stiffness or the. Abstract damping is an important issue in modelling dynamic systems. Obtained responses show that there is considerable effect of mode dependent damping on response of the system. Computation of rayleigh damping coefficients for large systems.
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 has been originally proposed and is suitable for single degree of freedom systems. 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. Straight beam with damping of rayleigh simscale documentation.
Gavin a rayleigh damping matrix is proportional to the mass and sti. Rayleigh damping is not applied to any line segment whose unstretched length is actively varying because of line feeding. Jun 22, 2014 damping, a property of the material and the structure, influences dynamic response. Equation 2 you can define rayleigh damping for linear and nonlinear dynamic studies. Learn about the sap2000 structural analysis and design program. 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. Damping ratio is a very important parameter for building structures in the analysis of dynamic response.
Pdf computation of rayleigh damping coefficients for. The stiffness proportional term contributes damping that is linearly proportional to. 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. The level of damping can be subjectively determined by noting the sharpness of resonant peak at f 1 figure 3. Rayleigh damping is a combina tion of mass proportional damping and stiffness proportional dampin g, as illustrated in figure 12. Rayleighs method requires an assumed displacement function. In that case, rayleigh damping should be compensated in order to obtain desired modal damping ratios. 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. Rayleigh damping rayleigh damping matrix c can be represented as the linear combination of the mass matrix m and the stiffness matrix k. Modal damping is used for responsespectrum and modal. Freque explic f2 f1 0 specifies the explicit frequencies f1 and f2 used for calculating the rayleigh damping coefficients.
It is also assumed that viscous damping can be modeled using a linear viscous damping term. 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. Initialstiffness damping generally leads to faster convergence during analysis, but may overestimate damping and hence be unconservative. It considers a massproportional and a stiffnessproportional damping in order to achive the real damping lets say 5%. Equivalent damping for displacementbased seismic design of. Compensation is exact if modal damping hypothesis 6 is veri. Rayleigh damping in abaqusexplicit dynamic analysis. For instance, a rayleigh damping model is widely used because of its excellent advantages 10. Equivalent damping for displacementbased seismic design of pilesupported wharves with soilpile interaction. For a nonconservative force the net work won a closed path is nonzero.
Modelling damping in linear dynamic systems final bachelor project dct report number. Mass proportional damping in nonlinear timehistory. 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. 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. The simulation results of simscale were compared to the results presented in case a and case b of sdls123. An extended rayleigh damping matrix, called caughey damping 1,2, can be computed from c m jxn 2 jn 1. 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. Determination of the rayleigh damping coefficients of steel. Modal damping vs rayleigh damping solidworks forums. Sap2000 allows users to either specify coefficients. 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. At least one study has indicated that when used improperly, superstructure rayleigh damping leads to excessive damping of the response of a baseisolated structure.
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