Vibroacoustic Simulation

1 Linear Systems, Random Process and Signals

Simple systems with properties constructed by lumped elements as masses, springs and dampers are a good playground to understand and investigate the physics of dynamic systems. Many phenomena of vibration as resonance, forced vibration and even first means of vibration control can be explained and visualized by these lumped systems.

In addition, a basic knowledge of signal and system analysis is required to put the principle of cause and effect in the right context. Every vibroacoustic system response depends on excitation by random, harmonic or specific signals in the time domain and we need a mathematical tool set to describe this.

An excellent test case to demonstrate and define the principle effects of vibration is the harmonic oscillator. It consists of a point mass, a spring and a damper. The combination of many point masses connected via simple springs and dampers provides some further insight into dynamic systems.

As those systems are described by components that have no dynamics in themselves they are called lumped systems. In principle all vibroacoustic systems can by modelled and approximated by this simplified approach.

1.1 The Damped Harmonic Oscillator

A realization of the harmonic oscillator is given by a concentrated point mass m fixed at massless spring with stiffness k_s as in Figure 1.1. The static equilibrium is assumed at u = 0 being the displacement in x-direction. A damper connecting mass and fixation creates ...