Damping may be specified for dynamic load cases. There are three distinct types of damping: modal damping, viscous proportional damping, and hysteretic proportional damping. The different types of damping apply to different types of load cases.
Damping is specified independently for each dynamic load case. In addition, damping may be specified for material properties and for link/support properties. Damping specified for these properties is additive to the load-case damping and affects all load cases.
Material damping is commonly used for portions of the model that are more heavily damped than the rest of the structure, such as soil regions. Link/support damping is typically used to represent discrete energy-dissipating members, or it can be used to represent radiation damping at the model boundaries
Modal damping is used for response-spectrum load cases and for modal time-history load cases. It can optionally be specified for direct-integration time-history load cases, in which case it is typically limited to the lower modes. Modal damping specified for the load case is additive to the material modal damping and the link/support modal damping.
Modal damping is given as a fraction of critical damping for each mode in the structure. On the Modal Damping form, damping may be specified in one of the following ways:
Constant for all modes
Linearly interpolated by period or frequency. Specify the damping value at a series of frequency or period points. Between specified points, the damping is linearly interpolated. Outside the specified range, the damping value is constant at the value given for the closest specified point.
Mass and stiffness proportional. This mimics the proportional damping described below for direct-integration, except that the damping value is never allowed to exceed unity.
In addition, damping overwrites may be specified. These are specific values of damping to be used for specific modes that replace the damping obtained by one of the methods above. The use of damping overwrites is rarely necessary, except perhaps to reduce the damping for long-period isolator modes.
This is also referred to as "composite modal damping from materials". If modal damping has been specified for a material property, it is converted automatically to composite modal damping for each element which uses that material. Any cross coupling between the modes is ignored. The modal damping values will generally be different for each mode, depending upon how much deformation each mode causes in the elements composed of the different materials.
For response-spectrum and linear modal time-history load cases, the damping coefficients specified for linear link/support elements, and the linear effective-damping coefficients that have been specified for nonlinear link/support elements, are automatically converted to modal damping. Any cross coupling between the modes is ignored. The added modal damping will generally be different for each mode, depending upon how much deformation each mode causes in the link/support elements.
For nonlinear modal time-history load cases, only the damping coefficients specified for linear link/support elements are converted to modal damping. For nonlinear link/support elements, any energy dissipation comes directly from the nonlinear behavior (viscous or hysteretic) of the element and is not converted into modal damping. The linear effective-damping coefficients are ignored.
Viscous proportional damping is used for direct-integration time-history load cases. Damping specified for the load case is additive to the material viscous damping and the link/support viscous damping.
The damping matrix is calculated as a linear combination of the stiffness matrix scaled by a user-specified coefficient, and the mass matrix scaled by a second user-specified coefficient.
The two coefficients may be specified directly, or they may be computed by specifying equivalent fractions of critical modal damping at two different periods or frequencies. Stiffness proportional damping is linearly proportional to frequency; mass proportional damping is linearly proportional to period.
Note that the initial stiffness of all elements and materials is used for calculating stiffness-proportional damping, not the current tangent stiffness. The only exception is when the tangent stiffness is zero and the corresponding force or moment is also zero, then the stiffness-proportional damping for that degree of freedom is set to zero.
If viscous proportional damping has been specified for a material property, it is applied (additively) to the stiffness and mass matrices for each element using that material in the same fashion that the load-case damping is applied to the entire structure.
For linear direct-integration time-history load cases, the damping coefficients specified for linear link/support elements, and the linear effective-damping coefficients that have been specified for nonlinear link/support elements, are added directly to the damping matrix of the structure.
For nonlinear direct-integration time-history load cases, the damping coefficients specified for linear link/support elements are added directly to the damping matrix of the structure. For nonlinear link/support elements, any energy dissipation comes directly from the nonlinear behavior (viscous or hysteretic) of the element. The linear effective-damping coefficients are ignored.
Hysteretic proportional damping is used for steady-state, power-spectral-density (PSD), and frequency-domain time-history load cases. These load cases are all linear and are solved in the frequency domain rather than the time domain. Damping specified for the load case is additive to the material hysteretic damping and the frequency-dependent link/support hysteretic damping.
The damping matrix is calculated as a linear combination of the stiffness matrix scaled by a user-specified coefficient, and the mass matrix scaled by a second user-specified coefficient. The two coefficients may be specified directly, or they may be computed by specifying equivalent fractions of critical modal damping at two different periods or frequencies. Stiffness proportional damping is independent of frequency; mass proportional damping is linearly proportional to period. The initial stiffness of all elements and materials is used for calculating stiffness-proportional damping. Note that mass-proportional hysteric damping is not commonly used.
If hysteretic proportional damping has been specified for a material property, it is applied (additively) to the stiffness and mass matrices for each element using that material in the same fashion that the load-case damping is applied to the entire structure. Note that material-proportional hysteric damping is not commonly used.
The basic property assigned to a link/support element does not provide any hysteretic damping, except for that which may come from the proportional damping specified for the load case as described below.
Instead, a separate frequency-dependent link/support property may optionally be assigned to each link/support element. This can be used to specify the stiffness and hysteretic damping for each degree of freedom, each as a function of frequency.
When a frequency-dependent link/support property is assigned to a given element, it completely determines the stiffness and damping used for a frequency-dependent load case. Stiffness-proportional damping from the load case is not considered. Only the mass and weight are derived from the basic link/support property.
When a frequency-dependent link/support property is not assigned to a given element, then stiffness-proportional hysteric damping from the load case is applied to the element.
Mass-proportional damping from the load case, if any, is applied to the link/support element regardless of whether or not a frequency-dependent property has been assigned to that element.