Exact free vibration analysis of open circular cylindrical shells by the method of reverberation-ray matrix

Abstract

Abstract:This paper is concerned with the free vibration analysis of open circular cylindrical shells with either the two straight edges or the two curved edges simply supported and the remaining two edges supported by arbitrary classical boundary conditions. Based on the Donnell-Mushtari-Vlasov thin shell theory, an analytical solution of the traveling wave form along the simply supported edges and the modal wave form along the remaining two edges is obtained. With such a unidirectional traveling wave form solution, the method of the reverberation-ray matrix is introduced to derive the equation of natural frequencies of the shell with different classical boundary conditions. The exact solutions for natural frequencies of the open circular cylindrical shell are obtained with the employment of a golden section search algorithm. The calculation results are compared with those obtained by the finite element method and the methods in the available literature. The influence of length, thickness, radius, included angle, and the boundary conditions of the open circular cylindrical shell on the natural frequencies is investigated. The exact calculation results can be used as benchmark values for researchers to check their numerical methods and for engineers to design structures with thin shell components.

Free Vibration Analysis of Circular Cylindrical Shells with Arbitrary Boundary Conditions by the Method of Reverberation-Ray Matrix

“…Li et al [31] investigated the influence on modal parameters of thin cylindrical shell under bolt looseness boundary. Yao et al [32] carried out the free vibration analysis of open circular cylindrical shells with either the two straight edges or the two curved edges simply supported and the remaining two edges supported by arbitrary classical boundary conditions based on the Donnell-Mushtari-Vlasov thin shell theory. As far as the researches of circular cylindrical shells are concerned, most of the existing works are limited to classical boundary conditions.…”

Dynamic performance of multi‐layered composite sandwich open cylindrical shells with double‐layered soft cores

“…Because there is scarcely any literature about MSCCOS, the published numerical results 22 of cylindrical laminated open shell and simulation solutions of MSCCOS are employed to validate the accuracy and effectiveness of deduced equations in this paper.…”

“…Abbas et al 21 employed the Runge–Kutta approach to carry out the vibration analysis in a high‐temperature field of cylindrical open shells based on the transfer matrix method. Yao et al 22 presented the vibration behavior of cylindrical open shells adopting the traveling waveform solution. To analyze the free vibration of open thick shell structures, Wang et al 23 formulated a precise three‐dimensional theoretical model.…”

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

“…This simple approach is adopted in this paper and the golden section search algorithm is introduced to determine the natural frequencies of the plate/shell coupled structure. The procedure for determining the natural frequencies of the plate/shell coupled structure is same to the one for free vibration analysis of open and closed circular cylindrical shell by MRRM presented in [52][53][54].…”