HBRP Publication Page 1-11 2019. All Rights Reserved Page 1 Research and Development in Machine Design Volume 2 Issue 2 Detailed Numerical Study of Free Vibration Analysis of Plates Kemparaju H.R 1 , Prasanta Kumar Samal 2 1 Associate Engineer, HCL Technology, Bangalore, India. 2 Associate Professor, Department of Mechanical Engineering, NIE Mysuru, India. E-mail: kemparajuhr@gmail.com, prasantaku.samal@gmail.com ABSTRACT Plates are widely used in aircraft, ship building, boiler and automobile applications. It is important to study the vibration characteristics of the plates in order to avoid the resonance in their working condition. Because catastrophic failure occurs in resonance condition due violent vibrations. So to avoid these resonance condition vibration analysis of plates are very important. In this article the modal frequencies and mode shapes of the plates were analysed numerically using ANSYS. Structural steel is considered as the plate material. All edges clamped (CCCC) and all edges free (FFFF) boundary conditions were considered for the study. The effect of parameters such as aspect ratio, thickness, area and shape of the plates on natural frequency was studied. The aspect ratios of 1, 1.5, 2 and 2.5 keeping the surface are same, is considered for the study. Plates of thickness 1 mm, 1.5 mm, 2 mm and 3 mm are analysed. The effect of shape of the plate is studied by considering various shapes like square, circular, equilateral triangle and right angular triangle with same area. It is observed that the natural frequency increases with increase of aspect ratio and thickness. As the surface area increases the natural frequency decreases. The values of natural frequencies of the plates descend in the order of circular, equilateral triangular, square and right angled triangular shapes for all edges free. Whereas the values of natural frequencies of the plates ascend in the order of circular, square, equilateral triangular and right angled triangular shapes for all edges fixed conditions. Keywords: Free vibration of plate, vibration of circular plate, vibration of triangular Plate, effect of thickness, aspect ratio, effect of cross sectional area, effect of boundary Conditions, ANSYS. INTRODUCTION Vibration analysis of a thick plate by finite element method using Mindlin plate theory has been carried out for rectangular and triangular element by Ivo Senjanovi et al. (2015). The finite element method and first order shear deformation theory is used to calculate the free vibration analysis of delaminated composite plate under all the edges simply supported and cantilever Boundary conditions by Bekelman et al. (2015). The plate vibration caused by acoustic emission of high frequency elastic wave is studied Amir Mostafapour (2016). He used Runge-Kutta method on MATLAB to solve the motion of equations on plate. The study of the free vibration analysis of a cantilever plate has been carried out by H.T. Saliba (1994).He wrote FORTRAN-77 code to generate mode shapes results then he compared the results with experimental results. Free vibration analysis of glass/epoxy laminated composite plates are studied by finite element analysis using ANSYS software by Dhanduvari Dinesh Kumar et.al. (2015). They compared the experimental results with numerical results. The effect of boundary condition on natural frequency of the plates also discussed. MinDING et,al, (2017) derived the nonlinear equations for thin elastic plates