LARGE-AMPLITUDE VIBRATIONS OF IMPERFECT ANTISYMMETRIC ANGLE-PLY LAMINATED PLATES

This paper deals with the large amplitude vibrations of imperfect antisymmetric angle-ply and symmetric cross-ply laminated plates using the von Kármán type non-linear plate model. The basic plate equations correspond to those of the parabolic shear deformation plate theory. Five governing differential equations of the plate are first reduced to a single non-linear time differential equation, using the single-mode approach to a simply supported plate. This equation involves the quadratic and cubic non-linearities for imperfect plates. Non-linear to linear frequency ratios have been obtained using the perturbation method and the exact method. Numerical results indicate that the perturbation methods are unreliable for certain plate problems and lead to wrong conclusions. It has been observed that whether the plate exhibits a hardening or softening type non-linearity depends on both the initial imperfection value and the amplitude of vibration. © 1993 Academic Press Limited.