Suboptimal rayleigh damping coefficients in seismic analysis of viscouslydamped structures. Note that when the leapfrog method is used with rayleigh damping, the damping ratio of the higher. The tcltk scripting language is free to download with the opensees source code. Dhanaji on application of rayleigh damping and numerical damping in finite elementdifference analysis. Damping is a function of velocity, so if there is no motion then there will be no damping. We have added three new modules into opensees based on the 2. Alpha and beta are constants used to set the amount of damping. Computation of rayleigh damping coefficients for the. K last committed can safely be used in lieu of k current for modeling rayleigh damping in opensees program. Each line type and turbine has structural damping properties determined by a named rayleigh damping coefficient data set.
Another issue is a damped multi degree of freedom system where the response has several resonance peaks at. Auto equaldof commands among quadquadup element nodes which share the same vertical y location. Topic 6 structural dynamics iii analysis of elastic mdof. If you have found any bug in the program or have any problem when using the program, please dont hesitate to contact me directly. Suitability for an incremental approach to numerical solution merits its use. An optimization method for the consistent evaluation of two rayleigh damping coefficients is proposed. 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.
October 2019 1 september 2019 1 july 2019 1 august 2018 1 july 2018 2 june 2018 2 may 2018 2 april 2018 2 march 2018 2 february 2018 19 january 2018 6. Off suppresses the calculation of rayleigh damping coefficients. Based on the above discussion, it is easy to also think of each mode damping independently. The region is specified by either elements or nodes, not both. 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. When using rayleigh damping in opensees, the damping matrix for an element or node, d is specified as a combination of stiffness and massproportional damping matrices. When the damping is based on the tangent stiffness and on updated frequencies based on this stiffness, virtually no artificial damping occurs. However, when the rayleigh damping model is adopted for an explicit algorithm. This form of c is orthogonal with respect to the system eigenvectors. Multiple such data sets can be defined, each with the following data. Gavin a rayleigh damping matrix is proportional to the mass and sti. We made the modal damping as a subclass of linearsoe based on the diagonal class because diagonalsoe is suitable for the leapfrog method.
Summary the rayleigh damping model, which is pervasive in nonlinear response history analysis. Modal damping vs rayleigh damping solidworks forums. Mass and stiffnessproportional damping, normally referred to as rayleigh damping, is commonly used in nonlineardynamic analysis. Topic 6 structural dynamics iii analysis of elastic mdof systems equations of motion for mdof systems. All other frequencies damp as well, but following the rayleigh model. Fedem, structural damping, rayleigh damping, frf, dynamic. Information on the abilities of the scripting language and on downloading it may be found through the opensees website or online at. This command is also used to assign rayleigh damping parameters to the nodes and elements in this region. Rayleigh damping is an empirical means by which to damp all frequencies. Gong, mechanical model of a hybrid nonlinear viscoelastic material damping device with its verifications, frontiers in materials, vol.
Application of rayleigh damping and numerical damping in. Of course, because there are only two parameters alpha and beta, you can only specify how two given frequencies should damp. Any excitation in the time domain will be followed by a decayed amplitude of response as energy is converted in the system. A simple gui for postprocessing data files from opensees analysis. The effects of viscous damping modeling methods on seismic.
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. Equation 1 the type of damping described by equation 1 is known as rayleigh or proportional damping. Suboptimal rayleigh damping coefficients in seismic. Freque explic f2 f1 0 specifies the explicit frequencies f1 and f2 used for calculating the rayleigh damping coefficients. 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 type of damping described by equation 1 is known as rayleigh or proportional damping. Opensees modeling design need opensees capability model nonlinear response and energy dissipation geometric and material nonlinear elements and hysteretic, rayleigh and viscous damping model variations in ballast, connectivity and static load patterns programmatic scripting of components and load patterns including simulated loads. Ahmad, damping is important whenever you are interested in the transient response of your structure. A shear wall element for nonlinear seismic analysis of. This enables one to model practically any type of variations in the modal damping.
In this paper a more general expression of the damping matrix is proposed while retaining the advantage of classical normal modes. This article intends to shed light on application of rayleigh and numerical damping in finite element and finite difference analyses. Rayleigh damping came out of linear theory massspringdashpot systems where it is easy to view each mode independently. Function loading type option plain pattern path timeseries added. The xaxis is time, and the yaxis is a nodal displacement. Nextfem designer can act as a pre and post processor for opensees. For instance, a rayleigh damping model is widely used because of its excellent advantages 10. Rayleigh damping in structural mechanics engineering. The corresponding viscous damping factor for mode j amounts to. Therefore, if using the region command to assign damping, the mass proportional damping and stiffness proportional.
As such, rayleigh damping models can provide a clear physical meaning and present a. This command is used to assign damping to all previouslydefined elements and nodes. This option is used to provide material damping for modebased analyses and for directintegration dynamic analysis in abaqusstandard and for explicit dynamic analysis in abaqus. There is a very limited number of studies on damping of higher modes. As you all know, there are two types of damping in a system subjected to dynamic loads. If elements are defined, the region includes these elements and the all connected nodes, unless the eleonly option is used in which case only elements are included. This outcome could be used for investigations of noise, harshness and fatigue. Rayleigh damping is characterized by the two constants a and b, whereas the damping coefficient of the concrete is 0. Xinzheng lu a, linlin xie a, hong guan b, yuli huang c, xiao lu d. This tutorial will use the following portal frame as driving example. 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.
By applying the modal coordinate transformation, the modal damping matrix c. Opensees software has been extended to include a damping matrix defined as the superposition of modal damping matrices. Explicit algorithm for collapse simulation comparison of computational speed algorithm damping model cost of each step explicitleapfrog rayleigh damping 2. Obtained responses show that there is considerable effect of mode dependent damping on response of the system. Selection of papers on opensees eos eurasian opensees. The program is for rayleigh damping coefficients calculation. Classical rayleigh damping is viscous damping which is proportional to a linear combination of mass and stiffness. The use of stiffness proportional material damping in abaqusexplicit may reduce the stable time increment dramatically and can lead to longer analysis times. A shear wall element for nonlinear seismic analysis of supertall buildings using opensees. That model has some fundamental differences from viscous or rayleigh damping. Evaluation of rayleigh damping and its influence on. Equation 2 you can define rayleigh damping for linear and nonlinear dynamic studies. Auto equaldof commands among nodes with different ndf that share the same location in general data window added.
Evaluation of the rayleigh damping model for buildings. Development and application of explicit methods in. Because mass proportional damping assigns damping to nodes with mass, opensees will ignore any mass proportional damping that is assigned using the rayleigh command in combination with the region command for a region of elements. If rayleigh is selected rayleigh damping is applied in a global way, i. Classical damping, nonclassical damping and complex modes. By applying the modal coordinate transformation, the modal damping matrix c becomes diagonal. Modes number m2 m1 0 specifies that the frequecies used for calculating the rayleigh damping coefficients are the eigenfrequencies of modes m1 and m2.
The simulation results of simscale were compared to the results presented in case a and case b of sdls123. The current title structural mechanics of a beam has nothing to do with it. During formulation, the damping matrix is assumed to be proportional to the mass and stiffness matrices as follows. It can also reduce computational efforts and prevent convergence difficulties. Modeling viscous damping in nonlinear response history analysis of. When the damping matrix is based on the tangent stiffness but the rayleigh proportionality constants are based on the initial stiffness, a significant but reduced amplification of damping occurs. The input parameters for the material should be as follows. Because the rayleigh damping model is not suitable for the leapfrog method, we added modal damping into opensees. Influence of mode dependent rayleigh damping on transient. After the definition of rayleigh damping, we propose a rheological interpretation of rayleigh damping.
Calculating rayleigh damping parameters posted nov 4, 2010, 12. Development and application of explicit methods in opensees for. For example the phase angle between the applied force and the displacement is different. To define rayleigh damping, you specify two rayleigh damping factors. Unintended consequences of modeling damping in structures.
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