Wave propagation in complex structures modelled by medium with internal variables

Abstract

AbstractGoverning equations for complex engineering structures are derived by means of the Hamilton variational principle under the assumption that the vibration field has a slowly varying component of an evolutionary type. This function is identified as the displacement of the primary structure, whereas the internal degrees of freedom model substructural vibrations. In the frequency domain of high modal overlap the secondary systems act as dynamic vibration absorbers with respect to primary structure. Wave propagation in the primary structures of complex structure is shown to be modelled by hyperbolic equations with source terms, the latter describing the backward effect of vibrating substructures on the primary structure. In order to take into account uncertain mechanical and spectral properties of real structures propagation of a wave packet in the structure is considered. The evolution of the amplitude of the propagating wave packet is shown to be governed by a boundary value problem of parabolic type. The approach developed presents an alternative to the vibrational conductivity approach and other techniques utilising various sorts of parabolic equations for describing energy propagation in complex structures.