An integral four-variable hyperbolic HSDT for the wave propagation investigation of a ceramic-metal FGM plate with various porosity distributions resting on a viscoelastic foundation

This work studies the dispersion relations of wave propagation in infinite advanced functionally graded (FG) ceramic-metal plates. A simple integral hyperbolic higher-order shear deformation theory (HSDT), with undetermined integral terms and only four unknowns, is used to formulate a solution for the waves’ dispersion relations. The effective functionally graded materials’ (FGM) properties follow the power-law with three different types of uneven porosity distributions. The effect of foundation viscosity is investigated by considering the damping coefficient in addition to Winkler’s and Pasternak’s parameters. The wave propagation’s governing equations are derived based on the present integral hyperbolic HSDT using Hamilton’s principle. The eigenvalue problem describing the porous FG plate dispersion relations resting on a viscoelastic foundation is analytically determined. The theory accuracy is validated by numerically comparing the results with previously published works. Finally, the influences of gradation power, porosity parameters, and the viscoelastic foundation parameters on wave propagation in an FG plate are examined and discussed.