Nonlinear primary resonance of spiral stiffened functionally graded cylindrical shells with damping force using the method of multiple scales

摘要

This paper studies a nonlinear primary resonance of spiral stiffened functionally graded (SSFG) cylindrical shell with viscos damping force. The cylindrical shell is subjected to the harmonic excitation. The material properties of the shell and stiffeners are assumed to be continuously graded in the thickness direction. The FG cylindrical shell with internal and external spiral stiffeners is investigated. The strain-displacement relations are obtained based on the von Karman nonlinear equations and the classical plate theory of shells. The smeared stiffener technique is used to model the under-studied SSFG cylindrical shell. The obtained partial differential equations of motion are discretized by means of the Galerkin method. In order to find the nonlinear primary resonance, the multiple scales method is adopted. The effects of various geometrical characteristics and material parameters on the nonlinear primary resonance response of spiral stiffened simply supported FG cylindrical shells are investigated.