Vibrations of sandwich plates with concentrated masses and spring-like inclusions

Linear dynamics of a sandwich beam (a plate of sandwich composition in one- dimensional cylindrical bending) bearing concentrated masses and supported by springs is described in the framework of the sixth order theory of multi layered plates. Analysis of the influence of a single inclusion and of a pa ir of identical inclusion upon vibrations of an infinitely long beam is per formed by the use of the Green function method. To construct the Green func tions, a dispersion polynomial is derived and normal modes are obtained. Pa rameters of propagating low-frequency waves are checked against results ava ilable in the literature. Then the Green functions for flexural and shear v ibrations of a beam excited by a point force or a point shear moment are co nsidered. Attention is focused on a comparison of forced vibrations of homo geneous beams and beams bearing concentrated masses supported by springs. T he role of interaction of dominant flexural waves with dominant shear waves near inclusions is discussed. Conditions of localization of flexural waves at these inhomogeneous are explored in respect of excitation parameters an d parameters of sandwich composition. Radiated acoustic power is computed i n the case of a homogeneous beam and in a trapped mode case to illustrate t he importance of the localization effect for structural acoustics. (C) 2000 Academic Press.