Analyzing nonlinear vibration of metal foam stiffened toroidal convex/concave shell segments considering porosity distribution

Abstract

Analysis of nonlinear vibration properties of stiffened toroidal convex/concave shells made of porous metal foam material in elastic medium has been performed in the present research. Metal foam is considered as porous material with uniform and nonuniform models. The governing equations of motion of eccentrically stiffened porous 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. The nonlinear governing equations are solved with the use of Jacobi elliptic functions to obtain the exact frequency–amplitude curves of the geometrically nonlinear metal foam toroidal shell. Presented results demonstrate the significance of porosity distribution, geometric nonlinearity, foundation factors, stiffeners and curvature radius on vibration characteristics of porous toroidal convex/concave shells.