Wave propagation in plate structures

Abstract

This study is concerned with dynamic response of complex plate structures, composed of rigidly connected thin plates, subjected to point or line loadings. The finite dement method is not recommended for this analysis since a very large number of meshes are needed to obtain accurate results in the high‐frequency range. Although the finite strip method only requires strip refinement in one direction, the computational efforts may be still tremendous if the structure is large or contains a large number of thin plates. However, the computational efforts can be greatly reduced when the finite strip method is combined with a new method developed by Yong and Lin [Y. Yong and Y. K. Lin, J. Sound Vib. 129(2), 99–118 (1989)]. In this approach, each strip with various boundary conditions is treated as a waveguide capable of transmitting different wave motions. A scattering matrix is defined to characterize wave motions at boundaries, locations where two plates are joined, and where the type of waveguides are changed. Thus a response at any location can be derived in terms of the scattering matrices. Three main advantages can be found in this analysis. First, the numerical computation is stable since it always proceeds in the directions of wave motions. Second, a strip refinement will not result in an increase in computer time. Third, the response is exact except for the modeling by finite strip approximation. Numerical examples will be given in light of the new analytical approach.