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An analytical solution for free vibration analysis of circular plates in axisymmetric modes based on the two variables refined plate theory

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Abstract

This paper presents, for the first time, an analytical solution for free vibrations of an isotropic circular plate in axisymmetric modes based on the two variables refined plate theory. This theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Governing equations are derived using Hamilton’s principle and an analytical method on the basis of using Bessel functions is introduced to solve them. By this procedure, final form of the governing equations is obtained in matrix form. These equations are solved for classical boundary conditions and comparison studies are performed to verify the validity of the present results. It is found that the results obtained using RPT and TSDT are close to each other. As a benchmark, numerical results are presented in a dimensionless form for various values of thickness to radius ratio.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

    Amir Hossein Shahdadi & Mohammad Ali Hajabasi

Authors
  1. Amir Hossein Shahdadi
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  2. Mohammad Ali Hajabasi
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Correspondence to Amir Hossein Shahdadi.

Additional information

Recommended by Associate Editor Ohseop Song

Amir Hossein Shahdadi was born in Mashhad (Iran) in 1987. He was graduated from Shahid Bahonar University of Kerman with B.Sc. in mechanical engineering in 2011. He also completed his education in M.Sc. in mechanical engineering at Shahid Bahonar University of Kerman in 2013. He is currently preparing himself for his Ph.D.

Mohammad Ali Hajabasi was born in Kerman (Iran). He has Ph.D. in mechanical engineering from Isfahan University of Technology. He is currently working as an assistant professor and also a faculty member of department of mechanical engineering at Shahid Bahonar University of Kerman. He is a supervisor for several theses in the fields of dynamics and vibration, computational mechanics, system modeling and optimization, multi-body dynamics, micro/nano mechanics and machine elements design.

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Shahdadi, A.H., Hajabasi, M.A. An analytical solution for free vibration analysis of circular plates in axisymmetric modes based on the two variables refined plate theory. J Mech Sci Technol 28, 3449–3458 (2014). https://doi.org/10.1007/s12206-014-0806-y

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  • DOI: https://doi.org/10.1007/s12206-014-0806-y

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