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Vibration of antisymmetric angle-ply composite annular plates of variable thickness

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Abstract

Based on first order shear deformation theory, free vibrational behaviour of antisymmetric angle-ply composite annular plate is investigated. The thickness variations are assumed to be linear, exponential and sinusoidal along the radial direction. The equilibrium equations are obtained from which the coupled differential equations are derived in terms of displacement and rotation functions. These functions are approximated using splines to obtain the system of algebraic equations in terms of spline coefficients where the equation becomes a generalized eigenvalue problem by combining the boundary conditions. This problem is solved for finding eigenfrequencies and corresponding eigenvectors. This study is conducted for clamped-clamped and clamped-free boundary conditions. Detailed parametric investigation is carried out to determine the influences of radii ratio, number of layers, ply orientations and materials on the frequencies of plates. The primary results of this study are compared with those available in the literatures.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, Skudai, Johor Bahru, Johor, Malaysia

    A. K. Nor Hafizah, K. K. Viswanathan & Z. A. Aziz

  2. UTM Centre for Industrial and Applied Mathematics, Ibnu Sina Institute for Scientific & Industrial Research, Universiti Teknologi Malaysia, 81310, Skudai, Johor Bahru, Johor, Malaysia

    A. K. Nor Hafizah, K. K. Viswanathan & Z. A. Aziz

  3. Kuwait College of Science and Technology, Doha District, Block 4, P.O. Box No. 27235, Safat, 13133, Kuwait

    K. K. Viswanathan

  4. Department of Naval Architecture and Ocean Engineering, Inha University, 100 Inharo, Nam-gu, Incheon, 22212, Korea

    J. H. Lee

Authors
  1. A. K. Nor Hafizah
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  2. K. K. Viswanathan
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  3. Z. A. Aziz
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  4. J. H. Lee
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Corresponding author

Correspondence to K. K. Viswanathan.

Additional information

Recommended by Associate Editor Kyeongsik Woo

Nor Hafizah Ahmad Kailani is a Ph.D. student in Applied Mathematics in Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Malaysia under Assoc. Prof. Dr. K.K.Viswanathan. She completed her Bachelor’s degree and Master’s degree in Mathematics from Universiti Teknologi Malaysia, Malaysia in 2012 and 2014, respectively. Her master’s degree versed on the application of finite element method in 2-dimensional heat distribution problems for irregular geometry. Her current work focuses on the study of vibration behavior for plates and shells using numerical approximation.

Kodakkal Kannan Viswanathan received his B.S. in Mathematics from University of Madras and M.S. in 1992 and Ph.D. in 1999 from Anna University, India. Later he was a Project Associate in Indian Institute of Science, Bangalore. He served as lecturer in Crescent Engg. College and as Asst. Professor in SRM University, India. He did his post doctoral research in Korea for three years. He served as Professor in the Dept. of Naval Architecture, Inha University, Incheon, Korea. After that, he worked at Universiti Teknologi Malaysia, Malaysia as an Associate Professor and Associate Fellow in UTMCIAM (UTM Centre for Industrial & Applied Mathematics). At present, he is working at Kuwait College of Science and Technology, Kuwait. His research areas of interest includes vibration of plates, shells and the application of numerical techniques in Engineering problems.

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Nor Hafizah, A.K., Viswanathan, K.K., Aziz, Z.A. et al. Vibration of antisymmetric angle-ply composite annular plates of variable thickness. J Mech Sci Technol 32, 2155–2162 (2018). https://doi.org/10.1007/s12206-018-0424-1

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  • DOI: https://doi.org/10.1007/s12206-018-0424-1

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