Dynamic instability analysis of tapered composite plates using Ritz and finite element methods

Tapered composite plates are widely used in civil, mechanical and aerospace structures such as robot arms, wing structures, helicopter yoke and turbine blade where the plate structure needs to be stiff at one location and flexible at another location. By terminating some plies at discrete locations, different types of ply drop-off can be obtained depending on the application. In the present work, the instability of tapered laminates under dynamic loading conditions is considered. Because of the complicated mechanical behavior of the tapered composite plate and the complexity of the analysis, no exact solution is available at present and therefore, Ritz method and finite element method have been used for the calculation of the dynamic instability regions. Solutions based on classical laminated plate theory have been developed first for vibration and buckling of uniform and tapered composite plates without in-plane forces. The effects on the laminate stiffness of the composite plates caused by the taper angle have been considered. Different configurations of tapered plates have been investigated. Then, based on the formulations for free vibration and buckling, the formulation for the dynamic instability analysis has been developed using Finite Element Method and Ritz method for both uniform-thickness and tapered composite plates based on classical laminated plate theory. The efficiency and accuracy of the developed formulation are established in comparison with available solutions for uniform-thickness laminates. The dynamic instability regions that serve as a measure of the degree of instability of the laminates are determined considering different boundary conditions, the tapered composite plate configurations, and the in-plane loading patterns. The NCT301 graphite-epoxy composite material is considered in the numerical stud