Vibroacoustic Simulation

3 Wave Propagation in Structures

3.1 Introduction

In comparison with the wave motion in structures the acoustic wave motion is simple. The equations are isotropic, the speed of sound is (in most cases) not dependent on frequency, and even for complex shapes the Green’s function provides a powerful tool to calculate the wave field. For structural waves the situation is different. In structures there is a variety of wave types described by displacements and rotations in several space dimensions or degrees of freedom. The chance to find a practicable analytical solution is low and solutions are only available for simple systems like straight bars, rectangular thin plates, or membranes. Thus, wave propagation in structures is a natural field for numerics: i.e. finite element methods (FEM) that discretize the real system into many small and simple elements that have an analytical solution or at least an approximation. The dynamics of the full system or the full mesh are defined by the complete set of all these elements.

This book is not about FEM, but we will often use a discrete form of the equation of motion or wave equation. There are two reasons for this:

Complex systems  The easiest way to describe the dynamics of a realistic technical system is by numerical methods; thus, there will always by a matrix description of the deterministic system. This is a standard approach in the industrial simulation of structural dynamics.

Formulation  There are many ways to describe dynamic ...