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The Duffing–Mathieu Equation Arising from Dynamics of Post-Buckled Beams

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Nonlinear Dynamics of Structures, Systems and Devices

Abstract

The nonlinear dynamics of a beam embedded in a viscoelastic continuous medium is considered. The beam undergoes large deflections induced by an axial harmonic excitation. The non-dimensional equation of motion describing the problem is approximated by a Duffing–Mathieu equation. Some analytical and numerical results are reported.

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References

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Authors and Affiliations

  1. Department of Structures for Engineering and Architecture (DiSt), University of Naples “Federico II”, Naples, Italy

    Enrico Babilio

Authors
  1. Enrico Babilio
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Correspondence to Enrico Babilio .

Editor information

Editors and Affiliations

  1. Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Rome, Italy

    Walter Lacarbonara

  2. Department of Mechanical Engineering, University of Maryland, College Park, MD, USA

    Balakumar Balachandran

  3. Department of Physics, Lanzhou University of Technology, Lanzhou, Gansu, China

    Jun Ma

  4. Department of Electrical Engineering, Polytechnic of Porto - School of Engineering (ISEP), Porto, Portugal

    J. A. Tenreiro Machado

  5. Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary

    Gabor Stepan

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Babilio, E. (2020). The Duffing–Mathieu Equation Arising from Dynamics of Post-Buckled Beams. In: Lacarbonara, W., Balachandran, B., Ma, J., Tenreiro Machado, J., Stepan, G. (eds) Nonlinear Dynamics of Structures, Systems and Devices. Springer, Cham. https://doi.org/10.1007/978-3-030-34713-0_27

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