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Axially Symmetric Vibrations of Circular Sandwich Plates of Linearly Varying Thickness

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Proceedings of the Third International Conference on Soft Computing for Problem Solving

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 258))

Abstract

In this paper axisymmetric vibration of circular sandwich plates with honeycomb core of linearly varying thickness has been studied. The facings are of the same thickness and of the same material, are treated as membranes. The facings take the shape of conical shell due to linear thickness variation in the core and hence membranes forces of the facings contribute to the transverse shear of the core. The equations of motion for such a plate have been derived by Hamilton’s energy principle. The frequency equations have been obtained by employing differential quadrature method for three different boundary conditions at the edge, namely, clamped, simply supported and free. The lowest three roots of these frequency equations have been obtained for various values of different plate parameters and reported as the frequencies for the first three modes of vibration. Three dimensional mode shapes for specified plates have been presented. Comparison of results with published work has been made.

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Acknowledgments

One of the authors, Rashmi Rani is thankful to Ministry of Human Resources and Development (MHRD), India for the financial support to carry out this research work.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 24766, India

    Rashmi Rani & Roshan Lal

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  1. Rashmi Rani
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  2. Roshan Lal
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Correspondence to Rashmi Rani .

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Editors and Affiliations

  1. Department of Paper Technology, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Millie Pant

  2. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Kusum Deep

  3. Department of Mathematics and Computer Science, Liverpool Hope University, Liverpool, United Kingdom

    Atulya Nagar

  4. Department of Applied Mathematics, South Asian University, New Delhi, India

    Jagdish Chand Bansal

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Rani, R., Lal, R. (2014). Axially Symmetric Vibrations of Circular Sandwich Plates of Linearly Varying Thickness. In: Pant, M., Deep, K., Nagar, A., Bansal, J. (eds) Proceedings of the Third International Conference on Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 258. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1771-8_15

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  • DOI: https://doi.org/10.1007/978-81-322-1771-8_15

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  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-322-1770-1

  • Online ISBN: 978-81-322-1771-8

  • eBook Packages: EngineeringEngineering (R0)

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