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Large Amplitude Free Vibration Analysis of Axially Functionally Graded Tapered Rotating Beam by Energy Method

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Vibration Engineering and Technology of Machinery

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 23))

Abstract

Geometrically nonlinear free vibration behaviour of axially functionally graded non-uniform rotating beams are investigated following variational form of energy method. Nonlinear strain displacement relations are employed to account for geometric nonlinearity present in the system. The static solution of the displacement field of the beam under centrifugal loading is obtained first and then the dynamic problem is formulated as an Eigenvalue problem based on the known static solution. The displacement fields are approximated by linear combination of orthogonally admissible functions and undetermined parameters. The method is validated successfully and results are presented in non-dimensional plane.

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology, Rourkela, 769008, Odisha, India

    Saurabh Kumar

  2. Department of Mechanical Engineering, Jadavpur University, Jadavpur, Kolkata, 700032, West Bengal, India

    Anirban Mitra

Authors
  1. Saurabh Kumar
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  2. Anirban Mitra
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Corresponding author

Correspondence to Anirban Mitra .

Editor information

Editors and Affiliations

  1. School of Mechanical, Aerospace and Civil Engineering (MACE), The University of Manchester, Manchester, United Kingdom

    Jyoti K. Sinha

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Kumar, S., Mitra, A. (2015). Large Amplitude Free Vibration Analysis of Axially Functionally Graded Tapered Rotating Beam by Energy Method. In: Sinha, J. (eds) Vibration Engineering and Technology of Machinery. Mechanisms and Machine Science, vol 23. Springer, Cham. https://doi.org/10.1007/978-3-319-09918-7_42

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  • DOI: https://doi.org/10.1007/978-3-319-09918-7_42

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09917-0

  • Online ISBN: 978-3-319-09918-7

  • eBook Packages: EngineeringEngineering (R0)

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