Thermo-mechanical free vibration analysis of porous solar FGM plates resting on Kerr’s foundation using a new logarithmic-hyperbolic shear deformation theory

A novel high-order shear deformation theory (HSDT) is established for the thermo-mechanical free vibration analysis of porous solar functionally graded material plates in a thermal environment. This HSDT is formulated using a logarithmic-hyperbolic function and eliminates the need for transverse shear correction factors. The displacement field is described by only four unknowns, with the third component of displacement divided into bending and shear components. The temperature-dependent material properties are represented by a simple power-law function, and the temperatures are distributed uniformly throughout the solar FGM plate thickness. Three models of porosity distribution, namely even, linear-uneven and trigonometric-uneven distributions, are employed to investigate the influence of porosities on the temperature-dependent material properties. The porous solar FGM plates are supported by three parameters of Kerr’s foundation. The equations of motion are derived by applying Hamilton’s principle, and Navier’s solution method is utilized to obtain closed-form solutions for these equations. The effects of temperature-dependent properties, power-law parameter, Kerr’s foundation and other factors on the thermo-mechanical vibration behavior are examined and validated by comparison with well-known theories in the literature. The current 2D-LHHSDT provides better results than various HSDTs when compared to the 3D-exact solutions.