Nonlinear vibrations of moderately thick orthotropic shallow spherical shells

Abstract

This paper deals with the effects of large amplitude on the flexural vibrations of shallow spherical shells. A shallow shell theory is presented for the geometrically nonlinear dynamic analysis of moderately thick orthotropic spherical shells. Transverse shear deformation and rotatory inertia effects are incorporated into the nonlinear equations of motion by means of tracing constants. The coupled set of nonlinear equations of motion are solved using Galerkin's method and solutions are obtained by employing the numerical Runge-Kutta integration procedure. Numerical results are presented for several cases of shallow spherical shells with various geometric and material properties. While the results indicate the well-known softening type behavior between nonlinear frequency and amplitude, certain interesting conclusions are presented for orthotropic shells. The general governing equations presented here can be readily specialized for isotropic shells, and linear vibration cases and they are in agreement with those available in the literature.