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 multilayered plates. Analysis of the influence of a single inclusion and of a pair of identical inclusion upon vibrations of an infinitely long beam is performed by the use of the Green function method. To construct the Green functions, a dispersion polynomial is derived and normal modes are obtained. Parameters of propagating low-frequency waves are checked against results available in the literature. Then the Green functions for flexural and shear vibrations of a beam excited by a point force or a point shear moment are considered. Attention is focused on a comparison of forced vibrations of homogeneous beams and beams bearing concentrated masses supported by springs. The 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 and parameters of sandwich composition. Radiated acoustic power is computed in the case of a homogeneous beam and in a trapped mode case to illustrate the importance of the localization effect for structural acoustics.