Nonlinear free vibration of laminated composite rectangular plates with curvilinear fibers

The geometrically nonlinear free vibration of laminated composite rectangular plates with curvilinear fibers is investigated. The assumptions of Von Kármán’s nonlinear thin plate theory are made. The problem is solved numerically using the hierarchical finite element method. The nonlinear equations of free motion are mapped from the time domain to the frequency domain using the harmonic balance method. The resultant nonlinear equations are solved iteratively using the linearized updated mode method. Results for the fundamental linear and nonlinear frequencies and associated mode shapes are obtained for fully clamped laminated composite square plates composed of shifted curvilinear fibers. The efficiency and accuracy of the hierarchical finite element technique is demonstrated through convergence and comparison studies. Contour plots of fundamental linear and nonlinear frequencies as a function of fiber orientation angles are presented. The fiber orientation angles and layup sequence are shown to affect the degree of hardening and mode shapes.