Coupled thermoelastic effect in free vibration analysis of anisotropic multilayered plates and FGM plates by using a variable-kinematics Ritz formulation

• A fully coupled thermoelastic formulation is developed.
• CUF-based 2D and quasi-3D theories are compulsory in thermoelastic investigations.
• The thermoelastic coupling is affected by the lamination angle.
• The thermoelastic coupling has a limited dependence on the length-to-thickness ratio.
• Antisymmetric cross-ply laminates show a higher thermoelastic coupling.
• Thermoelastic coupling is significant in FGMs.

A fully coupled thermoelastic formulation is developed to deal with free vibration analysis of anisotropic composite plates and isotropic/sandwich FGM plates. The proposed formulation is developed by combining refined hierarchical plate models and a trigonometric Ritz method. The temperature is considered as a primary variable and allows the evaluation of the temperature field effects in the free vibration analysis. The temperature profile across the plate thickness is always modeled with a layer-wise kinematics description, nevertheless both equivalent single layer and layer-wise approaches are properly and effectively used for the displacement variables. In the 2D and quasi-3D higher-order variable-kinematics plate theories, each displacement variable, in the displacement field, is treated independently from the others. Such artifice allows to select scrupulously each expansion order for each primary variable regarding to the required accuracy and the computational cost. So-called Ritz fundamental primary nuclei related to the coupled thermal and mechanical fields are generated by virtue of an unconventional principle of virtual displacement accounting for the internal thermal virtual work to reproduce the coupling effect. Each fundamental primary nucleus is mathematically invariant with respect to the used kinematics description, the employed expansion orders and the chosen Ritz functions. The thermoelastic coupling is investigated in terms of natural frequencies and the effect of stacking sequence and length-to-thickness ratio for lower and higher modes is discussed.