Study on the Use of Boundary Characteristic Orthogonal Polynomials in Determining the Fundamental Frequency of Rectangular Plates with Bidirectional Linear Thickness Variation

Abstract:

Free vibration of rectangular plates with linearly varying thickness is considered. Plates are important structural components used in aircrafts, bridges etc. and hence for their safe design, thorough vibration analysis is important. Many research and practical applications use plates of variable thickness due to economical usage of the material and increased strength. Vibration response of these types of plates is different from plates of uniform thickness, which makes their analysis critical. In this study, Boundary Characteristic Orthogonal Polynomials (BCOPs) in one and two dimensions have been used to obtain deflection shape function. The first member of the series is generated using the boundary conditions, in this case all edges clamped, which satisfies both the geometric boundary conditions and the natural boundary conditions. Gram Schmidt Orthogonalization for polynomials is used to generate the higher members of the shape function which only satisfy the geometric boundary conditions. Thickness variation considered for the plate is linear in both x and y direction. Natural frequencies were obtained by using Rayleigh-Ritz method. Natural frequencies were calculated by varying taper parameters for both directions and compared with those obtained with the case of uniform thickness. Natural frequencies were also found comparable with those obtained from Finite Element Analysis by using ANSYS.

• Periodical: Applied Mechanics and Materials (Volume 852)
• Pages: 518-524
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.852.518
• Online since: September 2016
• Authors: Tanmay Gupta, Bhagat Kewlani, Kiran D. Mali*
• Keywords: Boundary Characteristic Orthogonal Polynomials, Gram Schmidt Orthogonalization, Plate Vibration, Rayleigh-Ritz Method

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