Free vibration analysis of isotropic and composite folded plates using a shear flexible element

A high precision composite plate-bending element developed by Sheikh et al. has been applied to the free vibration analysis of isotropic and fibre-reinforced laminated composite folded plates. The in-plane displacements, transverse displacement and rotations of the normal have been taken as independent field variables and they have approximated with polynomials of different orders. Initially, the degrees of freedom of the element is 65, which is reduced to 54 by eliminating the degrees of freedom of the internal nodes through static condensation. To facilitate the condensation process, 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 mass matrix. Numerical examples of isotropic and composite one-, two-, and four-fold folded plates having different crank angles, fibre orientations, thickness ratios, number of layers and boundary conditions have been solved using the proposed element. The present results have been compared with those obtained from different sources. In all the cases the present element showed an excellent performances.