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Analytical approximation of nonlinear vibration of string with large amplitudes

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Abstract

Study of nonlinear problems in strings with large amplitude is a very important research area in many fields of physics and engineering. variational approach method (VAM) is in particular selected because the method is appropriate to solve nonlinear vibration of a constanttension string. VAM is an explicit method with high capability for resolving strong nonlinear oscillation system problems. It has been found that VAM is well suited for a range of parameters and the approximate frequencies and periodic solutions show a good agreement with the exact ones. This paper compares the various aspects of VAM in relative to exact approaches and higher-order approximate solutions for the constant-tension string. The comparison indicates that VAM is very fast, effective and convenient. The method does not require any linearization or small perturbation, and it leads to high accuracy of the solutions in a single iteration.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran

    Mojtaba Parvizi Omran

  2. Faculty of Industrial Design Engineering, Delft University of Technology, Delft, Netherlands

    Amin Amani

  3. Department of Mechanical and Structural Engineering and Material Technology, University of Stavanger, Stavanger, Norway

    Hirpa Gelgele Lemu

Authors
  1. Mojtaba Parvizi Omran
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  2. Amin Amani
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  3. Hirpa Gelgele Lemu
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Correspondence to Hirpa Gelgele Lemu.

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Recommended by Associate Editor Ohseop Song

Mojtaba Parvizi Omran received his B.S. in Mechanical Engineering from Iran University of Science and Technology in 2007. He then went on to receive his M.Sc. from Noshirvani University of Technology in 2010. He is currently candidate for Phd in Delft university of Technology.

Amin Amani received his B.S. in Mechanical Engineering from Noshirvani University of Technology in 2006. He then went on to receive his M.Sc. from Imam Hossein University in 2010. He is currently a Lecturer/Phd student in Delft university of Technology.

Hirpa G. Lemu received his MSc and PhD degrees from the Norwegian University of Science and Technology (NTNU) in 1997 and 2002 respectively. He is currently serving as associate Professor of Mechanical Design Engineering at University of Stavanger, Norway. His current research activities focus on simulation based design optimization, performance enhancement of energy conversion systems, multi-body dynamics simulation, analysis of material anisotropy, material modeling and analysis and simulation data management.

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Omran, M.P., Amani, A. & Lemu, H.G. Analytical approximation of nonlinear vibration of string with large amplitudes. J Mech Sci Technol 27, 981–986 (2013). https://doi.org/10.1007/s12206-013-0301-x

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  • DOI: https://doi.org/10.1007/s12206-013-0301-x

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