Non-linear vibration response of functionally graded circular cylindrical shells subjected to thermo-mechanical loading

Abstract

The analysis of the non-linear vibration response is carried out for functionally graded (FG) circular cylindrical shells subjected to thermal environment along with mechanical in-plane non-uniformly distributed loading along the edges and harmonic radial force. The temperature dependent material properties of the simply supported shell are assumed to vary in the radial direction according to power-law distribution. Based on the first-order shear deformation theory and von-Kármán type geometric nonlinearity, the strain-displacement relationships are established for circular cylindrical shells. The coupled governing equations of motion for functionally graded cylindrical shells are then derived using Hamilton’s principle. Employing Galerkin’s method, the coupled partial differential equations of motions are reduced to a set of non-linear ordinary differential equations. In order to obtain the free and forced vibration response of the FG shell, the incremental harmonic balance method, in conjunction with the arc-length method, is used. The non-uniform in-plane loading is converted to Fourier series and the pre-buckling analysis is performed to determine the stress distribution within the shell. The non-linear frequency-amplitude response is studied to examine the effects of volume fractions of the constituents, static partial edge loadings, thermal loads, and radial periodic loadings.