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Free vibration analysis of thin circular and annular plate with general boundary conditions

This paper presents a numerical analysis of free vibration of thin circular and annular plate using finite element method. The first five natural frequencies are presented for uniform annular plates of various inner-to-outer radius ratios, with nine possible combinations of free, clamped and simply supported boundary conditions at the inner and outer edges of plates. | Free vibration analysis of thin circular and annular plate with general boundary conditions Engineering Solid Mechanics 3 2015 245-252 Contents lists available at GrowingScience Engineering Solid Mechanics homepage www.GrowingScience.com esm Free vibration analysis of thin circular and annular plate with general boundary conditions S. Khare and N. D. Mittal Department of Mechanical Engineering Mulana Azad National Institute of Technology Bhopal India ARTICLE INFO ABSTRACT Article history This paper presents a numerical analysis of free vibration of thin circular and annular plate Received 6 April 2015 using finite element method. The first five natural frequencies are presented for uniform Accepted 12 June 2015 annular plates of various inner-to-outer radius ratios with nine possible combinations of free Available online clamped and simply supported boundary conditions at the inner and outer edges of plates. The 14 June 2015 Keywords accuracy of the method is established by comparing the results available in the literature. Circular and annular plate Results show that natural frequency parameter increases as the inner-to-outer radius ratio Natural frequency increases except in case of free boundary condition for which it decreases with the inner-to- Mode shape outer radius ratio. This result provides benchmark values that can be used to validate result Finite element method obtained by other approximate approaches such as finite difference method differential quadrature method and boundary element method. 2015 Growing Science Ltd. All rights reserved. 1. Introduction Circular and annular plates are the fundamental structural elements used in various engineering fields. The lateral vibration of such plates has been the subject of numerous studies. Yuan and Dickinson 1996 studied the natural frequency parameters for the free vibration of annular circular and sectorial plates using a Ritz solution. Vera et al. 1998 1999 studied free vibration of annular plates with