A refined theory with stretching effect for the dynamics analysis of advanced composites on elastic foundation

• This paper presents a free vibration analysis of functionally graded plates (FGPs).
• The plate rest on elastic foundation.
• The paper uses a higher order shear deformation theory (HSDT).
• The HSDT has 4 unknowns in which the stretching effect is included.
• The governing equations are obtained through the Hamilton’s principle.
• These equations are then solved via Navier-type, closed form solutions.

This paper presents a free vibration analysis of functionally graded plates (FGPs) resting on elastic foundation by using a higher order shear deformation theory (HSDT) in which the stretching effect is included. The highlight of this theory is that, in addition to including the thickness stretching effect (εzz ≠ 0), the displacement field is modeled with only 4 unknowns, which is even less than the first order shear deformation theory (FSDT). The elastic foundation follows the Pasternak (two-parameter) mathematical model. The governing equations are obtained through the Hamilton’s principle. These equations are then solved via Navier-type, closed form solutions. The fundamental frequencies are found by solving the eigenvalue problem. The degree of precision of the current solutions can be noticed by comparing it with the 3D and other closed form solutions available in the literature.