Transverse vibration of isotropic thick rectangular plates based on new inverse trigonometric shear deformation theories

• Free vibration of isotropic thick rectangular plates is investigated in present study.
• Four inverse trigonometric shear deformation theories have been proposed.
• Rayleigh–Ritz method is used in the modeling to obtain the eigenvalue problem.
• Relationships of earlier shear deformation theories with newer ones have also been noticed.
• New results for free vibration of plates are also reported with the 3-D mode shapes.

The present investigation deals with the proposition of four new inverse trigonometric shear deformation theories to study free vibration characteristics of isotropic thick rectangular plates subjected to various boundary conditions. The proposed theories exactly satisfy the transverse stress boundary conditions on the bottom and top surfaces of the plate, which were true in earlier shear deformation theories also. There are various methods to handle the said type of problems, but the Rayleigh–Ritz method is found to be efficient because it can very well handle all types of classical boundary conditions. Accordingly, the trial functions denoting the displacement components are expressed as the linear combinations of simple algebraic polynomials. The main objective of this investigation is to study the effects of geometric configurations and deformation theories on the frequency parameters as these may be important for design engineers. The new results for frequency parameters are incorporated after performing a test of convergence and validation in special cases with the available literature. 3-D mode shapes are also plotted to show the deflected shapes of the plate.