Nonlinear forced vibration response of bimodular laminated composite plates

The nonlinear forced vibration characteristics of bimodular material laminated cross-ply composite plates subjected to periodic excitation are investigated. The analysis is carried out using Bert’s constitutive model employing first order shear deformation theory based finite element method (FEM) including von Kármán geometric nonlinearity. The periodic response is obtained using shooting technique coupled with Newmark time marching, arc length and pseudo-arc length continuation algorithms. The second order differential equation of motion is solved directly without transforming to first order differential equations thereby preserving the banded nature of equations. The nonlinear periodic vibration characteristics such as steady state response history, phase plane plots and frequency spectra are presented. A detailed parametric study is carried out to analyse the influence of bimodularity, aspect ratio, thickness ratio, excitation amplitude, support conditions and lamination scheme on the forced vibration response. The significant difference in the positive/negative half cycle amplitudes due to bimodularity is predicted with/without geometric nonlinearity. The through the thickness variation of fiber direction normal strain is presented to show the extent of assignment of tensile/compressive properties and restoring force due to geometric nonlinearity. Further, the unstable regions of the frequency response curves between turning points could not be traced due to the perturbations stemming from the numerical truncation in finite element discretization/solution of equations and the bimodular action resulting in deviation of solution in shooting iterations leading to convergence failure.