Figure 1.1: Rayleigh Damping
DampingRatio,
ξ
Totalβ-dampingα-dampingω 1 ω 2Alpha damping can lead to undesirable results if an artificially large mass has been introduced into the
model. One common example is when an artificially large mass is added to the base of a structure to
facilitate acceleration spectrum input. (You can use the large mass to convert an acceleration spectrum
to a force spectrum.) The alpha damping coefficient, which is multiplied by the mass matrix, will produce
artificially large damping forces in such a system, leading to inaccuracies in the spectrum input, as well
as in the system response.
Beta damping and material damping can lead to undesirable results in a nonlinear analysis. These
damping coefficients are multiplied by the stiffness matrix, which is constantly changing in a nonlinear
analysis. Beta damping is not applied to the stiffness matrices generat ed by contact elements. The res-
ulting change in damping can sometimes be opposite to the actual change in damping that can occur
in physical structures. For example, whereas physical systems that experience softening due to plastic
response will usually experience a corresponding increase in damping, an ANSYS model that has beta
damping will experience a decrease in damping as plastic softening response develops.
1.4.2. Material-Dependent Alpha and Beta Damping (Rayleigh Damping)
Material-dependent damping allows you to specify alpha damping (α) or beta damping (β) as a mater-
ial property (MP,ALPD or MP,BETD). For multi-material elements such as SOLID65, β can only be specified
for the element as a whole, not for each material in the element. In these cases, β is determined from
the material pointer for the element (set with the MAT command), rather than the material pointed to
by any real constant MAT for the element .MP,ALPD and MP,BETD are not assumed to be temperature-
dependent, and are always evaluated at T = 0.0.
1.4.3. Constant Global Damping Ratio
The constant global damping ratio is the simplest way of specifying damping in the structure. It represents
the ratio of actual damping to critical damping, and is specified as a decimal number with the DMPRAT
command.DMPRAT is available only for spectrum, harmonic, and mode-superposition transient dynamic
analyses. Use MP,DMPR to define a material dependent damping coefficient.
1.4.4. Constant Structural Damping Coefficient
Structural damping allows you to incorporate hysteric behavior due to internal material friction by
specifying a coefficient on the stiffness matrix. In this type of damping, the damping force is proportional
to the displacement rather than the velocity as in the other damping options. Both constant structural
damping (DMPSTR) as well as material-dependent structural damping (MP,DMPR) are supported.
Release 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationOverview of Structural Analyses