Forced Vibration Analysis of Isotropic Thin Circular Plate Resting on Nonlinear Viscoelastic Foundation
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RESEARCH PAPER
Forced Vibration Analysis of Isotropic Thin Circular Plate Resting on Nonlinear Viscoelastic Foundation Saheed Afolabi Salawu1 · Gbeminiyi Musibau Sobamowo2 · Obanishola Mufutau Sadiq1 Received: 21 August 2019 / Accepted: 14 March 2020 © Shiraz University 2020
Abstract In this work, forced vibration analysis of isotropic thin circular plate resting on nonlinear viscoelastic foundation is investigated. The dynamic analogue of the Von Kármán equations is used to establish the governing equations. The system coupled nonlinear partial differential equations are transformed to system of nonlinear ordinary differential equation using Galerkin decomposition method. Consequently, the analytical solutions are provided using differential transformation method with Padè Laplace after treatment technique. The developed solutions are verified using the existing results in the literature, and good agreement is observed. Subsequently, the analytical solutions are used to investigate the effects of various parameters on the dynamic response of the plate. From the results, it is observed that nonlinear frequency ratio of vibrating circular plate increases with increased linear elastic foundation and tensile force. Nevertheless, it is established that the nonlinear frequency ratio of the plate decreases as nonlinear Winkler foundation and compressive force increase. Also, the results revealed that clamped edge and simply supported edge condition recorded the same softening nonlinearity. However, axisymmetric case of vibration gives lower nonlinear frequency ratio compared to symmetric case. Also, maximum deflection occurs when excitation force is zero; likewise attenuation deflection is observed due to the presence of viscoelastic foundation. It is expected that the findings from this research will enhance the design of structures subjected to vibration under where circular plates are used. Keywords Vibration · Isotropic circular plate · Deflection · Nonlinear viscoelastic foundation · Differential transform method List of Symbols h Plate thickness ρ Mass density D Flexural rigidity of isotropic plate Ω Dimensionless natural frequency ν Poisson’s ratio of isotropic plate Abbreviations a, b Dimension of the plate d First-order differential operator with respect to x dr * Saheed Afolabi Salawu [email protected]; [email protected] Gbeminiyi Musibau Sobamowo [email protected] Obanishola Mufutau Sadiq [email protected] 1
Department of Civil and Environmental Engineering, University of Lagos, Akoka 100213, Nigeria
Department of Mechanical Engineering, University of Lagos, Akoka, Lagos, Nigeria
2
w Transverse deflection x, y Rectangular space Cartesian coordinate along the length of thin plate
1 Introduction The dynamic behaviours of circular plates have been a subject of great research interest for the past few decades. In such research, it has been shown that thin circular plates may exhibit a flexural vibration, having the same order as the thickness of the plate. In that case, li
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