A quasi-3D trigonometric shear deformation theory for wave propagation analysis of FGM sandwich plates with porosities resting on viscoelastic foundation

Abstract In the present work, a quasi three-dimensional trigonometric shear deformation plate theory (quasi-3D TSDPT) is proposed for the wave propagation analysis of porous functionally graded material (FGM) sandwich plates resting on a viscoelastic foundation. The present plate theory accounts for the transverse shear and normal deformations by dividing the transverse displacement into bending, shear, and stretching components. Different types of FGM sandwich plates are taken into account. The porosities in the FGM layers of the sandwich structures are described by introducing the porosity volume fraction and the step function. The equations of motion governing the wave propagation behavior of porous FGM sandwich plates are derived by employing Hamilton’s principle. The analytical solutions to the wave dispersion relations are presented. Additionally, the parametric research is conducted to highlight the effects of the wave number, the porosity volume fraction, the viscoelastic foundation, the power-law exponent and the core-to-thickness ratio on the wave propagation. Results manifest that the influences of these parameters are significant on the wave propagation characteristics of porous FGM sandwich plates.