NONLINEAR FREE VIBRATION OF A MODERATELY THICK DOUBLY CURVED SHALLOW SHELL OF ELLIPTICAL PLAN-FORM

Abstract

The p-version of the finite element method is used in conjunction with the blending function method to investigate the nonlinear free vibration of a doubly curved shallow shell of elliptical plan-form. The effects of transverse shear deformations, rotary inertia, and geometrical nonlinearity are taken into account. The harmonic balance method is used to derive the equations of free motion. The resultant nonlinear equations are solved iteratively using the linearized updated mode method. The efficiency of the method is demonstrated through convergence study and comparison with published results. The effects of geometric parameters such as thickness, ellipse aspects, and curvatures on the backbone curves of a clamped doubly curved shallow shell of elliptical plan-form are studied. It is shown that the increase or decrease of the hardening behavior is dependent upon these parameters.