Natural Frequencies of Stiffenened and Unstiffened Laminated Composite Plates

In this study, the free vibration of laminated composite plates with and without stiffeners subjected to axial loads is carried out using finite element method. The plates are stiffened by laminated composite strip and Timoshenko beam. The plates and the strips are modeled with rectangular 9 noded isoparametric quadratic elements with three degrees of freedom per node and the Timoshenko beam is modeled with linear 2 noded isoparametric quadratic elements with 2 degrees of freedom per node. The effects of both shear deformation and rotary inertia are implemented in the modeling of plate and stiffener. The governing differential equations are obtained in terms of the mid-plane displacement components and shear rotations using Hamilton’s principle. The effects of axial tension and compression loads and stiffeners on the natural frequencies of the plate are investigated. Results indicate the tension loads and stiffeners will increase the natural frequencies while the compression loads reduce the natural frequencies. The buckling force of plate is computed by increasing the absolute value of compressive force until the first natural frequency tends to zero. Results of simple cases are compared with finding in the literature and a good agreement was achieved.