# Dynamics Analysis

## Setup

1. Specify the modal results to which the analysis is linked. The modal solution must exist in the current design study. In SimSolid, the time integration of the equations of motion is extremely fast and all modes are always included in the analysis.
2. For Frequency and Random Response, specify the frequency span upper and lower limits. For Transient response, specify Time span.
3. Specify damping using Rayleigh damping coefficients or Modal damping.
4. Select the Evaluate peak responses during solving check box to evaluate peak responses during solving phase.

See Create Analysis for additional information.

## Damping

Two methods to specify damping are supported.
Rayleigh Damping Coefficient
Assumes the damping matrix is proportional to the mass and stiffness matrices. You need to specify values for Mass (F1) and Stiffness (F2) in the Dynamics creation dialog to use this method.
Modal Damping
Creates critical damping ratio for each mode. You can specify this value in the Dynamics analysis creation dialog.

## Notes for Dynamics Analysis

1. When the base excitation type is displacement, the initial condition for displacement and velocity is always assumed to be zero.
2. In SimSolid, the boundary compatibility is approximately met. The response at the constrained end is not going to be an absolute zero but is relatively small compared to the peak responses.
3. Equivalent radiated power density is calculated as:
$\text{ERP}\text{ }\text{Density}\text{\hspace{0.17em}}\text{=}\text{\hspace{0.17em}}\text{ERPRLF}\text{\hspace{0.17em}}\text{*}\text{\hspace{0.17em}}\text{(0}\text{.5}\text{\hspace{0.17em}}\text{*}\text{\hspace{0.17em}}\text{ERPC}\text{\hspace{0.17em}}\text{*}\text{\hspace{0.17em}}\text{ERPRHO)}\text{\hspace{0.17em}}*\text{\hspace{0.17em}}{v}^{2}$
Where:
$v$
Normal velocity of the picked point
ERPC (Speed of sound in air)
343 m/s
ERPRHO (Density of air)
1.225 Kg/m3
$\text{ERP}\text{\hspace{0.17em}}\text{=}\text{\hspace{0.17em}}\text{ERPRLF}\text{\hspace{0.17em}}\text{*}\text{\hspace{0.17em}}\text{(0}\text{.5}\text{\hspace{0.17em}}\text{*}\text{\hspace{0.17em}}\text{ERPC}\text{\hspace{0.17em}}\text{*}\text{\hspace{0.17em}}\text{ERPRHO)}\text{\hspace{0.17em}}{\int }_{S}\text{ }{v}^{2}\text{ }ds$