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Three-dimensional magnetic field and thermal environment, and parameter uncertainty effects on nonlinear torsional vibration of an embedded rod composed of two dissimilar rods welded by friction welding

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Abstract

This study aims to investigate the nonlinear torsional vibration of an embedded rod composed of two dissimilar parts welded by friction rotary welding in a three-dimensional magnetic and thermal environment with considering uncertainty in parameters. The nonlinear strains are derived using the nonlinear Green–Lagrange strain relation. Hamilton’s principle is used to drive the nonlinear equation of motion and corresponding boundary conditions. The He variational method is used for solving the nonlinear equation of motion. An uncertainty analysis, as well as a sensitivity analysis, is used to demonstrate the effects of the uncertainty in the parameters and frequency sensitivities, respectively. In this study, the effects of magnetic field intensity, thermal stresses, rod length, elastic medium, nonlinear vibration amplitude, parameter uncertainties, and boundary conditions on the nonlinear torsional frequencies are investigated. Increasing the elastic medium stiffness and vibration amplitude at high temperatures results in increasing the nonlinear torsional frequencies.

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Acknowledgements

The authors are grateful to the University of Salahaddin-Erbil for supporting this work.

Funding

This research did not receive any specific grant from funding agencies.

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Authors and Affiliations

  1. Mechanical and Mechatronics Department, College of Engineering, Salahaddin University-Erbil, Erbil, 44001, Iraq

    Sardar S. Abdullah & Dilshad A. Mohammed

  2. School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, 11369, Iran

    Sardar S. Abdullah

  3. Chemical and Petrochemical Engineering Department, College of Engineering, Salahaddin University-Erbil, Erbil, 44001, Iraq

    Ahmed A. Ahmed

Authors
  1. Sardar S. Abdullah
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Correspondence to Sardar S. Abdullah.

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Abdullah, S.S., Mohammed, D.A. & Ahmed, A.A. Three-dimensional magnetic field and thermal environment, and parameter uncertainty effects on nonlinear torsional vibration of an embedded rod composed of two dissimilar rods welded by friction welding. J Braz. Soc. Mech. Sci. Eng. 45, 58 (2023). https://doi.org/10.1007/s40430-022-03981-2

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