Abstract
This article is concerned with 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. An analytical solution of the traveling wave form along the simply supported edges and the standing wave form along the remaining two edges is obtained based on the Flügge thin shell theory. With such a unidirectional traveling wave form solution, the method of reverberation-ray matrix is introduced to derive the equation of natural frequencies of the open circular cylindrical shell with various boundary conditions. Then, the golden section search algorithm is employed to obtain the natural frequencies of the open circular cylindrical shell. The calculation results are compared with those obtained by the finite element method and the method in available literature. Finally, the natural frequencies of the open circular cylindrical shell with various boundary conditions are calculated and the effects of boundary conditions on the natural frequencies are examined. The calculation results can be used as benchmark values for researchers to check their numerical methods and for engineers to design thin structures with shell components.
Highlights
Thin shells are extensively used in naval architecture and ocean engineering, as well as in civil, mechanical, and aeronautical engineering
To verify the validity of the method for determining natural frequencies of the Open circular cylindrical shells (OCCSs) presented in the preceding sections, the natural frequencies of the OCCS with all four simply supported (SS) edges are obtained and the results are compared with those obtained by finite element method (FEM) and the method adopted by Leissa
MRRM1 and MRRM2 represent the calculation results obtained by method of reverberation-ray matrix (MRRM) from the solutions for the OCCS with SS curved edges derived in section ‘‘Solutions for the OCCS with the curved edges supported by SSs’’ and the results obtained by MRRM
Summary
Thin shells are extensively used in naval architecture and ocean engineering, as well as in civil, mechanical, and aeronautical engineering. Nxx and Nuu denote the in-plane normal forces, Nxu and Nux the inplane shear forces, Mxx and Muu the bending moment, Mxu and Mux the torsional moment, and Qxz and Quz the out-of-plane shear forces acting on the cross sections perpendicular to the axial and circumferential directions, respectively.
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