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Pathfollowing of high-dimensional hysteretic systems under periodic forcing

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Abstract

The dynamic response and bifurcations of high-dimensional systems endowed with hysteretic restoring forces in all degrees of freedom are investigated. Two types of hysteresis models are considered, namely the Bouc–Wen model and a differential version of the so-called exponential model of hysteresis. The numerical technique tailored for tackling high-dimensional hysteretic systems is based on an enhanced pathfollowing approach based on the Poincaré map. In particular, a five-dof mass-spring-damper-like system, with each rheological element described by the Bouc–Wen or the exponential model of hysteresis enriched by cubic and quintic nonlinear elastic terms, is investigated and a rich variety of nonlinear responses and bifurcations is found and discussed.

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Acknowledgements

Some of the initial results of this paper were presented at the 24th Conference of the Italian Association of Theoretical and Applied Mechanics (AIMETA 2019), Rome, Italy, September 15–19, 2019. The work of WL and GF was partially supported by the PRIN Grant No. 2017L7X3CS-002—entitled 3D PRINTING: A BRIDGE TO THE FUTURE. Computational methods, innovative applications, experimental validations of new materials and technologies) which is gratefully acknowledged.

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Authors and Affiliations

  1. Dipartimento di Architettura, Roma Tre University, Via Madonna dei Monti 40, Roma, Italy

    Giovanni Formica

  2. Department of Structures for Engineering and Architecture, University of Naples Federico II, Via Claudio, 21, 80124, Naples, Italy

    Nicoló Vaiana & Luciano Rosati

  3. Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Via Eudossiana 18, Roma, Italy

    Walter Lacarbonara

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  1. Giovanni Formica
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  2. Nicoló Vaiana
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  4. Walter Lacarbonara
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Correspondence to Giovanni Formica.

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Formica, G., Vaiana, N., Rosati, L. et al. Pathfollowing of high-dimensional hysteretic systems under periodic forcing. Nonlinear Dyn 103, 3515–3528 (2021). https://doi.org/10.1007/s11071-021-06374-7

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  • DOI: https://doi.org/10.1007/s11071-021-06374-7

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