The influence of damping on waves and vibrations

This paper provides a unified approach for conventional and generalised lin ear models of viscoelastic constitutive behaviour. Creep, relaxation and hy steresis effects of materials and structures are described consistently. Ad vantages of the fractional derivative concept are outlined. Mathematical co nsequences resulting from operator non-locality in time domain and uniquene ss questions arising in frequency domain are addressed. The elastic-viscoel astic correspondence principle serves as a tool to obtain as well analytica l and numerical BEM and FEM solutions of wave propagation and vibration pro blems by transform methods. Characteristics of viscoelastic waves and vibra tions are discussed. The paper focusses on material damping but includes as pects of radiation damping description by discretisation methods as well. Important aspects of damping description are beyond the scope of selected t opics of this survey paper. This is why additional reading is recommended o n the following subjects: Thermo-viscoelasticity and non-linear viscoelasti city [3, 4, 21], determination of mechanical properties by experimental met hods [2, 4, 38, 43], damping devices and surface damping treatment [31, 38, 43], material damping data [3, 31] and structural damping [45] including t he nonlinear dissipation in mechanical joints such as bolted or riveted con nections [46-48]. A list which is by far not complete.