ANALYSIS OF VIBRATIONS AND ENERGY FLOWS IN SANDWICH PLATES BEARING CONCENTRATED MASSES AND SPRING-LIKE INCLUSIONS IN HEAVY FLUID-LOADING CONDITIONS
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文摘
Vibrations of and the energy propagation in an infinitely long fluid-loaded sandwich beam (a plate of the sandwich composition in one-dimensional cylindrical bending) bearing concentrated masses and supported by springs are described in the framework of the sixth order theory of multilayered plates coupled with the standard theory of linear acoustics. A sandwich plate is loaded by a layer of a compressible fluid which is bounded opposite to a plate side by a rigid baffle. The dispersion equation for a fluid-loaded sandwich plate is derived. The wave numbers (complex, pure real and pure imaginary) and relevant normal modes (both the travelling and the evanescent ones) are obtained. Their dependence on the parameter of a fluid's depth is studied. Then the Green matrix is constructed analytically as a linear combination of normal modes to describe the response of a plate and an acoustic medium to the point loading by a force or a moment. Continuity conditions at the loaded cross-section of a plate and in a fluid are formulated. Attention is focused at the selection of roots of the dispersion relation for the formulation of the continuity condition for a fluid at the loaded cross-section. The convergence rate of an approximate solution based on the modal composition of the Green matrix is estimated. The parametric study of the “structural” and the “fluid” energy flows in a fluid-loaded sandwich plate without inclusions is performed for various excitation conditions. Then the Green matrix method is applied to analyze the influence of a pair of identical inclusions on localization of vibrations (modal trapping) and energy flows. Conditions of localization of flexural waves at these inhomogeneities are explored.