Layerwise finite element for free vibration of geometricaly imperfect composite plates

After establishing the accuracy of the present layerwise model for linear and geometrically nonlinear bending, vibration and buckling analysis of laminated composite and sandwich plates subjected to mechanical load, as well as for thermal bending and buckling of laminated composite and sandwich plates, in this paper, free vibration of geometrically imperfect composite plate is presented. The mathematical model, based on Layerwise theory of Reddy, assumes layerwise variation of in plane displacements and constant transverse displacement through the thickness, linear strain displacement relations and linear orthotropic material properties. The Koiter’s model for initial geometric imperfection is adopted. In order to include various possible imperfection modes, such as sine type, local type and global type, an imperfection function in the form of the product of trigonometric function and hyperbolic function in (x,y) plane is used. The principle of virtual displacement (PVD) is used to derive Euler-Lagrange differential equation of motion. The weak form is discretized using nine node Lagrangian isoparametric finite element. Element stiffness matrix, initial stiffness matrix and element mass matrix are evaluated using 3x3 Gauss-Legendre integration scheme, for 2D quadratic in-plane interpolation. Consistent element mass matrix is implemented in order to preserve the total mass of the element. The original MATLAB computer program is coded for the finite element solution. The effects of imperfection amplitude on fundamental frequencies is analysed. The accuracy of the numerical model is verified by comparison with the available results from the literature. It is found that geometric imperfection greatly affect the free vibration behaviour of composite laminates and should be taken into account when designing safe and functional structures.