Thermo-mechanical vibration analysis of bi-directional functionally graded plates in bi-directional temperature fields

Abstract

Characterized by continuous material gradient in two spatial directions, bi-directional functionally graded materials (2D FGMs) are born to adapt to the bi-directional temperature fields (2D TF) near the stagnation point of hypersonic vehicle wing leading edges. Their unique configuration mitigates peak thermal stresses and homogenizes stress distribution, which exhibits promising potential in hypersonic vehicles. Existing studies predominantly focused on uniform/unidirectional TFs or axisymmetric geometries, with natural frequencies derived numerically. This study investigated the dynamic characteristics of 2D FGM square plates with temperature-dependent material properties subjected to 2D TFs that approximating service conditions for the first time. First, a 2D TF model conforming to the heat conduction equation was established. Second, governing equations were derived based on the power-law function, four-variable shear deformation theory, and Hamilton’s principle. Subsequently, an analytical framework integrating the Levy method, the perturbation approach, and the state-space method was developed and validated. Finally, the compound parametric effects of TFs, power-law indexes, and material gradients were investigated. It was found that, frequencies and thermally induced forces are more sensitive to the temperature gradient along the thickness direction; The 2D material gradient coordinated with the 2D TF and effectively suppresses thermally induced forces across most regions.