Prog. Civil Struct. Eng. 1(1): 1-11 (2021) Progress in Civil and Structural Engineering Available at https://asps-journals.com  Corresponding author. E-mail address: paramgajbhiyeamdsvnit@gmail.com This work is licensed under a Creative Commons Attribution 4.0. License (CC BY 4.0) http://creativecommons.org/licenses/by/4.0/ PROGRESS IN CIVIL AND STRUCTURAL ENGINEERING | PCSE | ISSN 2716-800X (PRINT) Available online at https://asps-journals.com/index.php/pcse https://doi.org/10.38208/pcse.v1i1.2 Free Vibration Analysis of Thick Isotropic Plate by Using 5th Order Shear Deformation Theory Param D. Gajbhiye  1 , Vishisht Bhaiya 1 , Yuwaraj M. Ghugal 2 1 Department of Civil Engineering, Sardar Vallabhbhai National Institute of Technology, Surat-395007, G.J., India 2 Department of Applied Mechanics, Government Engineering College, Karad, Satara-415124, M.S., India Received 27 April 2020 Revised 15 January 2021 Accepted 20 January 2021 Published online: 26 February 2021 Abstract: In the present study, a fifth order shear and normal deformation theory is presented for free vibration analysis of simply supported thick isotropic square plates. Governing equations and boundary conditions are obtained using the virtual work principle. The bending, thickness shear, and thickness stretch frequencies are obtained using the Navier solution technique for simply supported thick isotropic plates. The eigenvalue problem in this study is solved using the MATLAB program. Numerical results for free vibration analysis include the effect of side to thickness ratio for simply supported thick isotropic square plates. The bending and thickness shear mode frequencies obtained using the present theory are in excellent agreement with those of exact solution and other refined shear deformation theories. Further, for the first time, the thickness stretch mode frequencies are also presented using this theory. Keywords Thick isotropic plate 5th OSDT Free Vibration Navier solution Non-dimensional frequencies © 2021 The authors. Published by Alwaha Scientific Publishing Services, ASPS. This is an open access article under the CC BY license. 1. Introduction Plates are the most widely used structural element in the field of engineering. Behaviour of the thick plates either, isotropic or anisotropic, subjected to static and dynamic loading requires the use of refined shear deformation theories, as the classical plate theory neglects the effect of transverse shear deformation generated in the thick plates. The classical plate theory based on the Navier- Kirchhoff hypothesis [1, 2] under predicts deflections and over predicts natural frequencies. Further, the primary concern of the researchers is to develop an equivalent one-dimensional (1-D) and two-dimensional (2-D) theories for the three-dimensional (3-D) plate problems. Timoshenko and Woinowsky-Krieger [3] presented flexural and buckling solutions for different types of thin plates subjected to various static loading and boundary conditions. Jemielita [4] introduced a brief review of the development in the theory of plates formulation from 1789-1988. Refined shear deformation theories presented by Reissner [5], Levy [6], Mindlin [7], Hencky [8] and Kromm [9] are the refinement of the classical plate theory (CPT) considering the effect of transverse shear deformation. Shear deformation theories depending on the assumption of primary variables can be classified as stress-based and displacement-based theories. Reissner’s theory is stress based and Hencky, Mindlin theories are displacement-based theories. The first refined higher order theory was proposed by Levy in 1877 [6]. A century later, Lo et al. [11, 10] established a compatible higher order theory for laminated plates. The proposed theory considered the effects of transverse normal strain, transverse shear deformation, in-plane and transverse displacements with respect to the thickness