Stochastic vibration mechanisms in irregular coupled plate of supersonic porous functionally graded materials with temperature gradients

The porous irregular functional gradient material (FGM) coupled plates, composed of two arbitrary quadrilateral plates coupled at any angle, are widely used in aerospace applications and equipment such as hypersonic vehicles. This paper investigates the stochastic response mechanisms of the porous irregular FGM coupled plate under aerothermal environments and base acceleration excitations. Three typical geometric models are established to validate the universality of the present method. The equations derived from supersonic piston theory and Mindlin plate theory incorporate temperature-dependent material properties. Subplate displacements are approximated using the first-kind Chebyshev polynomials, with irregular domain integrals resolved through coordinate transformations. Sufficient comparisons with the finite element method (FEM) and published literature confirm the accuracy and computational efficiency of this approach. The resulting systematic framework enables stochastic response analysis in analogous complex structures. Numerical discussions are conducted to analyze the effects of FGM gradient p, porosity ζ, coupling angle θ, boundary conditions, and temperature variations ΔT on the stochastic response, establishing practical tools for optimizing and conducting rapid integrity assessment of such structures.