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Open AccessArticle

Reconstruction of Governing Equations from Vibration Measurements for Geometrically Nonlinear Systems

1
Politecnico di Bari, Department of Mechanics Mathematics and Management, Via Orabona 4, 70125 Bari, Italy
2
Department of Mechanical Engineering, Am Schwarzenberg-Campus 1, Hamburg University of Technology, 21073 Hamburg, Germany
3
Department of Mechanical Engineering, Imperial College London, Exhibition Road, London SW7 2AZ, UK
*
Authors to whom correspondence should be addressed.
Lubricants 2019, 7(8), 64; https://doi.org/10.3390/lubricants7080064
Received: 28 June 2019 / Revised: 30 July 2019 / Accepted: 31 July 2019 / Published: 5 August 2019
(This article belongs to the Special Issue Tribology and Contact Dynamics)
Data-driven system identification procedures have recently enabled the reconstruction of governing differential equations from vibration signal recordings. In this contribution, the sparse identification of nonlinear dynamics is applied to structural dynamics of a geometrically nonlinear system. First, the methodology is validated against the forced Duffing oscillator to evaluate its robustness against noise and limited data. Then, differential equations governing the dynamics of two weakly coupled cantilever beams with base excitation are reconstructed from experimental data. Results indicate the appealing abilities of data-driven system identification: underlying equations are successfully reconstructed and (non-)linear dynamic terms are identified for two experimental setups which are comprised of a quasi-linear system and a system with impacts to replicate a piecewise hardening behavior, as commonly observed in contacts. View Full-Text
Keywords: nonlinear dynamics; system identification; sparse regression; time series; geometric nonlinearity; contact nonlinear dynamics; system identification; sparse regression; time series; geometric nonlinearity; contact
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MDPI and ACS Style

Didonna, M.; Stender, M.; Papangelo, A.; Fontanela, F.; Ciavarella, M.; Hoffmann, N. Reconstruction of Governing Equations from Vibration Measurements for Geometrically Nonlinear Systems. Lubricants 2019, 7, 64.

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