*DAMPING

Keyword type: model definition, if structural damping: material

This card is used to define Rayleigh damping for implicit 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 $\left [ M \right ]$:

$$\left [ C \right ] = \alpha \left [ M \right ] + \beta \left [ K \right ].$$ (467)

The damping force satisfies:

$$\lbrace F \rbrace = \left [ C \right ] \lbrace v \rbrace,$$ (468)

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 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:

$$\lbrace F \rbrace_e = i \zeta_e \left [ K \right ]_e \lbrace x \rbrace_e,$$ (469)

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:

• *DAMPING
• Enter ALPHA and BETA and their values for Rayleigh damping or STRUCTURAL and its value for structural damping.

Example:

*DAMPING,ALPHA=5000.,BETA=2.e-3

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

Example:

*DAMPING,STRUCTURAL=0.03

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

Example files: beamimpdy1, beamimpdy2.