Novel results in vibration analysis of nonlinear laminated composite beams (LCBs)

Abstract

This study investigates vibrations of the laminated composite beam (LCB) subjected to axial load and settled on Winkler–Pasternak elastic foundation. The beam model is of Euler–Bernoulli type with cubic order nonlinear elastic load. Two different boundary conditions are considered: (i) Simply Supported (S–S) and (ii) Clamped–Clamped (C–C) ones. Mathematical model of the asymmetric LCB is a partial differential equation. Applying Galerkin procedure, the model is converted into a strong nonlinear ordinary equation. In the paper, the new analytical method, dubbed as the Max–Min Approach (MMA), is adopted to provide more accurate nonlinear analysis of beams. The analytical solution is inferred to investigate the effects of axial force and essential elasticity parameters of foundation on the nonlinear response of the beams. Analytical results are compared with numerical solutions and show good agreement. In addition, the results are compared with previously published ones. It is concluded that MMA used in LCB gives more accurate results than the previously used analytic methods and is practical applicable. The method can be easily extended to high nonlinear vibration problems in LCB under different boundary conditions.