Nonlinear dynamical analyses of eccentrically stiffened functionally graded toroidal shell segments surrounded by elastic foundation in thermal environment

Abstract

Abstract In this study, the nonlinear vibration and dynamic buckling of eccentrically stiffened functionally graded toroidal shell segments surrounded by an elastic medium in thermal environment are presented. The governing equations of motion of eccentrically stiffened functionally graded toroidal shell segments are derived based on the classical shell theory with the geometrical nonlinear in von Karman-Donnell sense and the smeared stiffeners technique. Furthermore, the dynamical characteristics of shells as natural frequencies, nonlinear frequency–amplitude relation, nonlinear dynamic responses and the nonlinear dynamic critical buckling loads evaluated by Budiansky-Roth criterion are considered. The effects of characteristics of functionally graded materials, geometrical ratios, elastic foundation, pre-loaded axial compression and temperature on the dynamical behavior of shells are investigated.