scope:

Introduction

All dynamic processes in mechanic systems are more or less damped. Consequently, damping is highly relevant in those fields of technology and applied physics which deal with dynamics and vibrations. These include

• machine-, building-, and structural dynamics,
• system dynamics,
• control engineering, and
• technical acoustics,

because damping in these cases often has a considerable effect on the time history, intensity, or even the existence of vibrations. Important applications are:

• transient vibrations (transient effects associated with the onset or decay of vibrations, shock-induced vibrations,reverberation effects)
• resonance vibrations (unavoidable with random excitation)
• wave propagation
• dynamic-stability problems

Accordingly, a multitude of scientific publications dealing with damping, or taking it into account at least, are found in technical literature. Due to different theory approaches, objects, and task definitions in the applications listed above, the designations, the characterisation of damping, the experimental techniques, and the analytical and numerical methods are not harmonised.

The dynamic behaviour of damped structures can, in special cases, be calculated using generally valid material laws for inelastic materials based on continuum mechanics taking into account boundary effects (e.g. joints). In general, this approach is too elaborate or expensive, or not at all practicable. In most cases, therefore, phenomenological equivalent systems or mathematical models tailored to the task definition are used which are only valid assuming a special state of stresses and/or a special time history. Harmonic (sinusoidal) time histories are a preferred special case where complex quantities describe the elastic and damping properties. These depend on a number of parameters: material data, rate of deformation, frequency, temperature, number of load cycles, etc. In the case of nonlinear behaviour there is also a dependence on the amplitude.

For certain problems, it is sufficient to state, for one deformation cycle, the energy dissipated in a unit volume or within the system, or the energy released into the environment at the system boundaries, often related to a conveniently chosen elastic energy in a unit volume or in the system as a whole. In structural dynamics, the use of modal damping ratios has proven useful, which do no longer contain detailed information about the damping.