# Transient Response Analysis

## Overview

Transient response analysis is the most general method for computing forced dynamic response. The purpose of a transient response analysis is to compute the behavior of a structure subjected to time-varying excitation. The transient excitation is explicitly defined in the time domain. All of the loads applied to the structure are known at each instant in time. Loads can be in the form of applied forces and enforced motions (see Enforced Motion). The results obtained from a transient response analysis are typically displacements, velocities, and accelerations of grid points, and forces and stresses in elements.

In NX Nastran, use:

- SOL 109 to perform direct transient response analysis.
- SOL 112 to perform modal transient response analysis.

The direct transient response method performs a numerical integration on the complete coupled

equations of motion. The modal transient response method utilizes the mode shapes of the

structure to:

- Reduce the problem size because not all of the modes are typically calculated or retained.
- Uncouple the equations of motion when either no damping or only modal damping is used.

The physical solution is then obtained through the summation of the individual modal responses. The choice of method depends upon the structure and the nature of the loading. The solutions to direct and modal transient response analysis are always real responses. Thus, complex terms in the equation of motion like those resulting from structural damping are not allowed.

**Direct Transient Response Analysis (SOL 109)**

In direct transient response analysis, the structural response is computed by solving the equation of motion using direct numerical integration.

**Modal Transient Response Analysis (SOL 112**)

Modal transient response analysis is another method for computing the transient response of a structure. This method uses the mode shapes of the structure to reduce the size, uncouple the equations of motion (when no damping or only modal damping is used), and make the numerical integration more efficient (when the equations of motion are uncoupled). Because the mode shapes are typically computed as part of the characterization of the structure, modal transient response analysis is a natural extension of a normal modes analysis.