Physical damping

You can define damping in physical terms and then let Simcenter Nastran use a modal reduction to treat the damping matrix in modal space.

You can include this physical viscous and/or hysteretic (structural) damping in your response evaluations. Before solving the model, you must add the appropriate Simcenter Nastran parameter in the solution attributes or add the appropriate elements (such as dampers or bushings) or material damping in your FEM as described in Damping.

Damping matrix-to-ratio conversion in Simcenter Nastran

Simcenter Nastran converts the physical damping matrices to modal space using the following equations.

Modal viscous damping matrix:

Modal structural (hysteretic) damping matrix:

Because Response Dynamics uses critical damping ratios for viscous damping and loss ratios for hysteretic damping, Simcenter Nastran converts the modal matrices cm and km (which in general are not diagonal) to damping ratios using these equations:

where:

Z	= Viscous damping ratio matrix
G	= Structural loss ratio (hysteretic damping)
Ω	= Diagonal matrix of the modal frequencies
m	= Modal mass matrix
cm	= Modal viscous damping matrix
km	= Modal structural damping matrix
k	= Modal stiffness matrix

In general, the viscous damping ratio and structural loss ratio matrices are not diagonal, but Response Dynamics uses only the diagonal terms for the response evaluation.

Damping by event type in response evaluations

In a response evaluation, the software uses physical damping differently depending on the analysis event type.

Frequency events

The forms of Z and G (discussed in the previous section) are used.

Transient events

Only viscous damping can be used in the motion equations. Therefore, for Transient events, Response Dynamics converts structural damping to an equivalent viscous damping for the response evaluation. The equivalent viscous damping is calculated as:

Random events

For modal response evaluations, the forms of Z and G are used.

Response Spectrum events

Because Response Dynamics begins the evaluation from excitations of SRS functions or DDAM, damping effects are not used during the response evaluation. However, modal damping is used when you use the CQC or NRL evaluation methods with the Evaluate Peak Response command (in which damping is used as a correction factor used in the summation of the modal peak responses).

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Fast Fourier Transformation (FFT)

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Modal reduction

Mode acceleration method

Mode displacement method

Modal response calculation for transient analysis

Modal response calculation for frequency analysis

Random vibration

Response spectrum analysis

Modal damping

Shell stress resultants

Theory of Fast RMS modal response computing

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Physical damping, Simcenter 3D 2021.1 Series

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