An analytical approach: Nonlinear vibration of imperfect stiffened FGM sandwich toroidal shell segments containing fluid under external thermo-mechanical loads

Abstract

An analytical study to the nonlinear vibration of imperfect stiffened FGM sandwich toroidal shell segment containing fluid in external thermal environment is approached in this present. The toroidal shell segments consist of two types convex shell and concave shell which are reinforced by ring and stringer stiffeners system. Material properties of shell are assumed to be continuously graded in the thickness direction. Based on the classical thin shell theory with geometrical nonlinearity in von Karman-Donnell sense, Stein and McElman assumption, and the smeared stiffeners technique theoretical formulations are established. In addition, the dynamical pressure of fluid is taken into account. The fluid is assumed to be non-viscous and ideal incompressible. The nonlinear vibration analyses of full-filled fluid toroidal shell segment are solved by using numerical method fourth-order Runge-Kutta. Furthermore, effects of geometrical and material parameters, imperfection, fluid and change of temperature field on the nonlinear vibration responses of shells are shown in obtained results. It is hoped that the obtained results will be used as benchmark solutions for an analytical approach of fluid-structures vibration in further research.