Nonlinear forced vibrations of sandwich conical shells with metal foam cores and axially functionally graded faces under external excitation

Abstract

This paper analyzes the nonlinear forced vibration of sandwich conical shells with a metal foam core and axially functionally graded (AFG) faces under external excitation. The mechanical properties of the faces are assumed to vary along the shell’s length. For the metal foam core, three porosity distributions are considered. After deriving the structural relations and assuming the displacement field based on the first-order shear deformation theory (FSDT), the nonlinear dynamic equations of the system are obtained using Hamilton’s principle. First, the shell’s mode shape functions are obtained using the generalized differential quadrature (GDQ) method. Afterward, the shell’s nonlinear transverse motion equation is solved using the Galerkin and harmonic balance methods. After validating the results, the effects of physical and geometrical parameters, including porosity coefficient, porosity distribution, longitudinal FG power index, core-to-total thickness ratio, and semi-vertex angle, on the frequency and force–amplitude response curves are investigated.