Free vibration analysis of plate/shell coupled structures by the method of reverberation-ray matrix

Abstract

This paper is concerned with free vibration analysis of plate/shell coupled structures with two opposite edges simply supported by the method of reverberation-ray matrix. The equations of motion of the flat plate and the open circular cylindrical shell, respectively based on the classical thin plate theory and the Flügge thin shell theory, are introduced. Analytical solutions of the combination of a traveling wave form along the circumferential direction and a standing wave form along the axial direction are obtained. The method of reverberation-ray matrix is applied to derive the equation of the natural frequencies for the plate/shell coupled structures. The semi-analytical natural frequencies are obtained with the employment of the golden section search algorithm. The semi-analytical calculation results of three typical plate/shell coupled structures are presented and the results are compared with those obtained by the finite element method. The comparison shows that the calculation results obtained in this paper are of high accuracy and that the formulation presented in this manuscript are validated for free vibration analysis of plate/shell coupled structures.