*MODAL DAMPING

Keyword type: step

This card is used within a step in which the *MODAL DYNAMIC or *STEADY STATE DYNAMICS procedure has been selected. There are two optional, mutually exclusive parameters: RAYLEIGH and MODAL=DIRECT (default).

If MODAL=DIRECT is selected the user can specify the viscous damping factor $\zeta$ for each mode separately. This is the default. Direct damping is not allowed in combination with nonzero single point constraints.

If RAYLEIGH is selected 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 $\left [ M \right ]$:

$$\left [ C \right ] = \alpha \left [ M \right ] + \beta \left [ K \right ].$$ (186)

The coefficients apply to all modes. The corresponding viscous damping factor $\zeta_j$ for mode j amounts to:

$$\zeta_j=\frac{\alpha}{2 \omega_j}+ \frac{\beta \omega_j}{2}.$$ (187)

Consequently, $\alpha$ damps the low frequencies, $\beta$ damps the high frequencies.

The *MODAL DAMPING keyword can be used in any step to redefine damping values defined in a previous step.

First line:

• *MODAL DAMPING,RAYLEIGH
• Enter any needed parameters and their values.

Second line if MODAL=DIRECT is selected (or, since this is default, if no additional parameter is entered):

• lowest mode of the range
• highest mode of the range (default is lowest mode of the range)
• viscous damping factor $\zeta$ for modes between (and including) the lowest and highest mode of the range

Repeat this line if needed.

Second line if RAYLEIGH is selected:

• not used (kept for compatibility reasons with ABAQUS)
• not used (kept for compatibility reasons with ABAQUS)
• Coefficient of the mass matrix $\alpha$.
• Coefficient of the stiffness matrix $\beta$.

Example:

*MODAL DAMPING,RAYLEIGH
,,0.,2.e-4

indicates that the damping matrix is obtained by multiplying the stiffness matrix with $2 \cdot 10^{-4}$

Example files: beamdy3, beamdy4, beamdy5, beamdy6.