Accurate free vibration analysis of thermo-mechanically pre/post-buckled anisotropic multilayered plates based on a refined hierarchical trigonometric Ritz formulation

An advanced variable-kinematics trigonometric Ritz formulation built in the extended framework of the Carrera Unified Formulation (CUF) is developed to cope with free vibration response of anisotropic composite plates in a thermo-mechanical pre/post-buckled state. By using the CUF it is not only possible to introduce different expansion orders for each displacement unknown, but also to retain or discard a particular term with respect to its effectiveness and independently form its location in the displacement field generating the so-called mixed axiomatic/asymptotic theories. The proposed formulation is based on Ritz fundamental primary and secondary stiffness, mass and initial stress nuclei which are built in a unified framework that allows them to be invariant regarding to the used kinematic description, the expansion order adopted for each displacement component and the chosen trial functions. Refined equivalent single layer, zig-zag and layer-wise models are assessed by comparison with the 3D elasticity solution. Convergence and accuracy of the presented formulation are critically examined. Several in-plane mechanical load conditions combined with temperature variations are applied and their influence upon the free vibration response is studied. The effects of significant parameters such as stacking sequence, orthotropic ratio and length-to-thickness ratio on the circular frequency parameters are deeply investigated.