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Vibration of Pre-Loaded Shallow Circular Arches

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Nonlinear Dynamics of Structures, Systems and Devices

Abstract

We study dynamics of pre-stressed pinned shallow slender circular arches by one-dimensional field equations, simplified and solved by perturbation. The static response to a uniform load and small imperfections is found: the transverse displacement depends in closed form on the load. The first two frequencies of small vibration about the deformed shape, plus possible bifurcations in terms of the initial geometry and the pre-load are found.

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Authors and Affiliations

  1. Istanbul Technical University, Istanbul, Turkey

    Uğurcan Eroğlu

  2. University “La Sapienza” and National Group for Mathematical Physics, Roma, Italy

    Giuseppe Ruta

Authors
  1. Uğurcan Eroğlu
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  2. Giuseppe Ruta
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Corresponding author

Correspondence to Giuseppe Ruta .

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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Eroğlu, U., Ruta, G. (2020). Vibration of Pre-Loaded Shallow Circular Arches. 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_24

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