Introduction

A dynamic simulation is one in which inertia forces are included in the dynamic equation of equilibrium:

where

M

is the mass of the structure,

$\ddot{u}$

is the acceleration of the structure,

I

are the internal forces in the structure, and

P

are the applied external forces.

The expression in the equation shown above is nothing more than Newton's second law of motion ($F=ma$).

The inclusion of the inertial forces ($M\ddot{u}$) in the equation of equilibrium is the major difference between static and dynamic analyses. Another difference between the two types of simulations is in the definition of the internal forces, I. In a static analysis the internal forces arise only from the deformation of the structure; in a dynamic analysis the internal forces contain contributions created by both the motion (i.e., damping) and the deformation of the structure.

Natural frequencies and mode shapes
Modal superposition