Keyword type: model definition, if structural damping: material

This card is used to define Rayleigh damping for implicit and explicit dynamic calculations (*DYNAMIC) and structural damping for steady state dynamics calculations (*STEADY STATE DYNAMICS).

For Rayleigh damping there are two required parameters: ALPHA and BETA.

Rayleigh damping is applied in a global way, i.e. the damping matrix $ \left [ C \right ]$ is taken to be a linear combination of the stiffness matrix $ \left [ K \right ]$ and the mass matrix $ \left [ M \right ]$:

$\displaystyle \left [ C \right ] = \alpha \left [ M \right ] + \beta \left [ K \right ].$ (617)

The damping force satisfies:

$\displaystyle \lbrace F \rbrace = \left [ C \right ] \lbrace v \rbrace,$ (618)

where $ \lbrace v \rbrace$ is the velocity vector. For Rayleigh damping only one *DAMPING card can be used in the input deck. It applies to the whole model.

For explicit dynamic calculations only mass proportional damping is allowed, i.e. $ \beta$ must be zero.

For structural damping the damping is a material characteristic. Each material can have its own damping value. There is one required parameter STRUCTURAL, defining the value $ \zeta$ of the damping. For structural damping the element damping force is displacement dependent and satisfies:

$\displaystyle \lbrace F \rbrace_e = i \zeta_e \left [ K \right ]_e \lbrace x \rbrace_e,$ (619)

where $ i=\sqrt{-1}$, $ [K]_e$ is the element stiffness matrix, and $ \lbrace x
\rbrace_e$ is the element displacement vector. $ \zeta_e$ is the structural damping value for the material of element $ e$ (default is zero). The global damping force is assembled from the element damping forces.

First line:



indicates that a damping matrix is created by multiplying the mass matrix with $ 5000.$ and adding it to the stiffness matrix multiplied by $ 2 \cdot 10^{-4}$



defines a structural damping value of 0.03 (3 $ \%$). This card must be part of a material description.

Example files: beamimpdy1, beamimpdy2.