Vibroacoustic Simulation

5 Structure Systems

5.1 Introduction

The complex situation of wave propagation in structures becomes even worse for closed structural systems. When specific features like holes, rigs, beading or any complicated shape is given, this is definitely the world of numerical methods. Current finite element methods (FEM) in combination with pre and post processors can handle very complex and large systems as for example trains or aircraft. But, the modelling procedure, the creation of the mesh, and the population of the property and material database are time consuming. Analogous to fluid systems we stay with academic cases to work out the full frequency range.

Even though we are not dealing with the details of FEM we will rely on the discrete representation of systems as introduced in section 1.4. Some of the following treatments rely on the discrete matrix formulation of structures, that is the dynamic stiffness matrix. Thus, the principle definitions are given without description of the finite element method. Please rely for example on the textbook from Bathe (1982) for more details. In Chapter 3 the equations of motion are expressed in displacements $u,v,w$, the components of the stress tensor for the bulk material ${\sigma }_{ij}$ and forces and moments $F_i,M_i$. Rotations ${\beta }_i$ are approximated as the derivative of displacement components.

In finite element theory the rotational components are considered as dedicated degrees of freedom. Thus, in this chapter the natural coordinates will therefore ...