Non-linear free vibration analysis of laminated composite cylindrical/hyperboloid shell panels based on higher-order shear deformation theory using non-linear finite-element method

Abstract

In this article, the non-linear free vibration analysis of the laminated composite shallow cylindrical/hyperboloid shell panels is attempted by taking geometric non-linearity in Green—Lagrange sense. A higher-order shear deformation theory is employed to model the shell panel flexure. A set of non-linear governing equations is derived using a variational approach. A non-linear finite-element model is proposed and applied to obtain discretized non-linear equations. Typical numerical examples have been solved using a direct iterative technique. Effects of lamination schemes, modular ratio, amplitude ratio, thickness ratio, and various boundary conditions on the frequency ratio (non-linear frequency to linear frequency) are examined in detail. The results are compared with those available in the literature. These show the importance and necessity of the Green—Lagrange-type non-linearity especially when the shell panel undergoes large deformation.