Study nonlinear vibration of cross‐ply laminated plates using scale models

Abstract

This article describes the establishment of necessary similarity conditions for geometrically nonlinear vibrations of thin cross‐ply laminated plates. The Von‐karman's strain‐displacement relations have been employed to model structural nonlinearity of the system. The Galerkin procedure is used to reduce the nonlinear partial differential equations to a nonlinearly second‐order ordinary differential equation. An analytical investigation based on the direct use of the governing equations of the systems is undertaken to derive the necessary scaling laws and similarity conditions. In this study, a set of scaling laws are introduced that can predict the nonlinear free vibration frequency of the prototypes by projecting the frequency of the model, accurately. The effects of distorted models with relaxations in the number of plies, stacking sequence, and different vibration amplitudes are studied. The results presented herein indicate that models with different relaxations can predict the nonlinear vibration frequency of prototypes with good accuracy. POLYM. COMPOS., 35:752–758, 2014. © 2013 Society of Plastics Engineers