Free Flexural Vibration of Composite Plates in Different Situations Using a High Precision Triangular Element

Abstract

A high precision, thick-plate element developed by D. Sengupta has been applied to the free vibration analysis of laminated composite plates with necessary addition and modification. The effect of shear deformation has been incorporated in the formulation, taking the transverse displacement and rotations of the normal as independent field variables. These are approximated with polynomials of different orders, which has made the element free from locking in shear. The element contains internal nodes. The degrees of freedom of these nodes have been eliminated through condensation in its final form. To facilitate the condensation, an efficient mass lumping scheme has been recommended to form the mass matrix having zero mass for the internal nodes. Recommendation has also been made for the inclusion of the rotary inertia in the lumped mass matrix. Numerical examples of plates having different shapes, boundary conditions, thickness ratios, fiber orientations and number of layers have been solved. Examples of plates having internal cutout and concentrated mass have also been studied. The results obtained in all cases have been compared with those obtained from other sources to show the accuracy and range of applicability of the element.