Ultrasound Propagation in Viscoelastic Material GuidesCastaings, M.1, Predoi, M.V.2, Hosten, B.1 1 Laboratoire Mécanique Physique, Univ. Bordeaux 1, UMR CNRS 5469, Talence, France
2 Catedra de Mecanica, Universitatea Politehnica Bucuresti, Bucuresti, Romania
Wave propagation in elastic waveguides is a problem of constant interest from the last decades. Several numerical approaches exist. The most intuitive uses time-marching routines that solve the equations of dynamic equilibrium and supply displacements of the structure nodes as time functions. This procedure is usually time and memory consuming due to huge number of temporal iterations required for defining properly time histories. Moreover, it does not allow the natural wave attenuation produced in viscoelastic material guides to be easily taken into account.
Another approach consists in decomposing the problem into a number of stationary problems in the frequency domain. Time histories can therefore be retrieved at any point of the structure by simple inverse Fourier transforms. Both time and memory requirements are largely reduced due to very small numbers of frequency components necessary for representing classical time histories. Moreover, solving the equations of dynamic equilibrium in the frequency domain allows the attenuation of wave modes to be correctly modelled. This also allows absorbing regions to be defined for simulating infinitely long waveguides.
Examples are given for an elastic, anisotropic material plate by comparing the two procedures and then by considering the viscoelasticity of this material.