Natural frequencies and critical temperatures of functionally graded sandwich plates subjected to uniform and non-uniform temperature distributions

Free vibration and thermal stability analyzes of functionally graded (FG) sandwich plates are carried out by using the advanced Hierarchical Trigonometric Ritz Formulation (HTRF). Refined higher-order kinematics plate models accounting for through-the-thickness deformation are developed within the framework of Carrera’s Unified Formulation (CUF). The Principle of Virtual Displacements (PVD) is used as variational statement to develop the HTRF. Uniform, linear and non-linear temperature rises through-the-thickness layer plate direction are considered. The non-linear temperature distribution is given in different forms: (i) power law through-the-thickness variation; (ii) solution of the one-dimensional Fourier heat conduction equation; (iii) sinusoidal. The effect of initial thermal stresses on the free vibration behavior of the FG sandwich plates is investigated. Accuracy of the presented formulation is discussed in details. Moreover, the effects of volume fraction index, aspect ratio, boundary conditions, length-to-thickness ratio, sandwich plate type and temperature distributions through-the-thickness plate direction, for both natural frequencies and critical temperatures are thoroughly investigated.