The influence of damping on waves and vibrations

This paper provides a unified approach for conventional and generalised linear models of viscoelastic constitutive behaviour. Creep, relaxation and hysteresis effects of materials and structures are described consistently. Advantages of the fractional derivative concept are outlined. Mathematical consequences resulting from operator non-locality in time domain and uniqueness questions arising in frequency domain are addressed. The elastic-viscoelastic correspondence principle serves as a tool to obtain as well analytical and numerical BEM and FEM solutions of wave propagation and vibration problems by transform methods. Characteristics of viscoelastic waves and vibrations are discussed. The paper focusses on material damping but includes aspects of radiation damping description by discretisation methods as well. Important aspects of damping description are beyond the scope of selected topics of this survey paper. This is why additional reading is recommended on the following subjects: Thermo-viscoelasticity and non-linear viscoelasticity [3, 4, 21], determination of mechanical properties by experimental methods [2, 4, 38, 43], damping devices and surface damping treatment [31, 38, 43], material damping data [3, 31] and structural damping [45] including the nonlinear dissipation in mechanical joints such as bolted or riveted connections [46-48]. A list which is by far not complete.