Flügge shell theory and solution for the vibration analysis of a thin elastic cylindrical panel of varying curvature

Abstract

In this paper, the free vibration behavior of isotropic and orthotropic cylindrical shell panels with variable curvature subjected to certain ends boundary conditions is analyzed by the transfer matrix technique and solved by the Romberg integration approach. Flügge’s shell theory is employed to model the governing three-dimensional equations of vibration and Fourier’s approach is used to deform the displacement fields as trigonometric functions in the longitudinal direction. As a result of a semi-analytical procedure is conducted, the coupled governing equations of panel problem can be written in a matrix partial differential equation of first order with variable coefficients and reduced from the two-dimensional problem to one-dimensional one which is solved numerically as an initial-value problem. The proposed model is applied to get the natural frequencies and mode shapes for the vibration behavior of two-side simply-supported cylindrical panels with simply-supported, free-free, clamped-free and clamped-clamped ends boundary conditions lying at their curved edges. The sensitivity of the vibration behavior to the variety of curvature, panel parameters and material orthotropy of shell is studied.