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The free vibration problem of one-layered and two-layered metallic plates is investigated in this work. The thermomechanical effect is evaluated using a fully coupled thermomechanical model. The free frequency values of fully coupled problems are compared to the values of the pure mechanical problems. In pure mechanical models, the displacement is the only primary variable of the problem, while in fully coupled thermomechanical models, the temperature is also considered as a primary variable and the effect of the thermomechanical stiffness is evaluated. The thermoelastic coupling usually provides higher frequencies with respect to the pure mechanical case because it acts like a thermal source, which is proportional to the strain rate, which leads to a bigger global stiffness of the structure. Both thermomechanical and mechanical models are developed in the framework of Carrera's Unified Formulation (CUF). CUF permits several refined two-dimensional theories to be obtained with orders of expansion in the thickness direction, from linear to fourth-order, for both displacements and temperature. Both equivalent single layer and layer-wise approaches are considered for the multilayered plates. The thermomechanical effect is investigated, in terms of frequencies, for thick and thin one-layered and two-layered plates, and for lower and higher modes. It has mainly been concluded that the thermomechanical coupling: (a) Is correctly determined if both the thermal and mechanical parts are correctly approximated; (b) Is small for each investigated case; (c) Influences the various vibration modes in different ways; and (d) Has a limited dependence on the considered case, but this dependence vanishes if a global coupling is considered. Only fully coupled thermomechanical models allow to analyze this type of problem. The effect of the thermomechanical coupling on higher-order modes can only be investigated using refined two-dimensional theories.

This work deals with the vibration problem of metallic plates subjected to combined axial, biaxial and shear in-plane loading. Various type of boundary conditions are considered. Results related to thin plate theories and shear deformation theories are compared to a third-order plate theory including the thickness stretching effects. The Finite Element Method (FEM) is applied on the basis of Carrera Unified Formulation kinematic assumptions. FE matrices are computed by referring to the four-node element. The mixed interpolation of tensorial components technique is used in order to contrast the shear locking for both classical and refined theories. The influence of the in-plane loading (combined axial, biaxial and shear) on plate undamped natural frequencies is illustrated and discussed. Various plate geometries and boundary conditions are considered.