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Parameter sensitivity of cantilever beam with tip mass to parametric excitation

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Abstract

The sensitivity of the response of a parametrically excited cantilever beam with a tip mass to small variations in elasticity (stiffness) and the tip mass is performed. The governing equation of the first mode is derived, and method of multiple scales is used to determine the approximate solution based on the order of the expected variations. We demonstrate that the system can be designed so that small variations in either stiffness or tip mass can alter the type of bifurcation. Notably, we show that the response of a system designed for a supercritical bifurcation can change to yield a subcritical bifurcation with small variations in the parameters. Although such a trend is usually undesired, we argue that it can be used to detect small variations induced by fatigue or small mass depositions in sensing applications.

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Acknowledgements

The authors would like to thank Dr. Mohammad Younis for sharing his expertise and providing valuable suggestions. The first author would also like to thank Dr. Ayoub Boroujeni for providing useful insights on carbon fiber/epoxy resin composites.

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Authors and Affiliations

  1. Department of Biomedical Engineering and Mechanics, Virginia Tech, 495 Old Turner Street, Norris Hall, Blacksburg, VA, 24060, USA

    Vamsi C. Meesala

  2. Department of Civil, Environmental and Ocean Engineering, Stevens Institute of Technology, 1 Castle Point Terrace, Hoboken, NJ, 07030, USA

    Muhammad R. Hajj

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  1. Vamsi C. Meesala
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  2. Muhammad R. Hajj
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Correspondence to Vamsi C. Meesala.

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Meesala, V.C., Hajj, M.R. Parameter sensitivity of cantilever beam with tip mass to parametric excitation. Nonlinear Dyn 95, 3375–3384 (2019). https://doi.org/10.1007/s11071-019-04760-w

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  • DOI: https://doi.org/10.1007/s11071-019-04760-w

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