## *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 ]. (810)

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}. (811)

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.