ANALYSIS OF THE NONLINEAR VIBRATIONS OF UNSYMMETRICALLY LAMINATED COMPOSITE BEAMS

Large-amplitude free vibrations of unsymmetrically laminated beams using von Karman large deflection theory are investigated herein. One-dimensional finite elements based on classical lamination theory, first-order shear-deformation theory, and higher-order shear-deformation theory having 8, 10, and 12 degrees of freedom per node, respectively, are developed to bring out the effects of transverse shear on the large-amplitude vibrations. Because of the presence of bending-extension coupling, the bending stiffness of an unsymmetric laminate is direction dependent yielding different amplitudes and spatial deformations for the positive and negative deflection half-cycles. The problem is studied by reducing the dynamic nonlinear finite element equations to two second-order ordinary nonlinear differential equations using converged normalized spatial deformations in the positive and negative deflection half-cycles. These modal equations of motion are solved using the direct numerical integration method and results are presented for various boundary conditions, lay-up sequences, and slenderness ratios. Inadequacies in the results of approximate methods are highlighted.