Approximating piecewise nonlinearities in dynamic systems with sigmoid functions: advantages and limitations

Martinelli, C., Coraddu, A. and Cammarano, A. (2023) Approximating piecewise nonlinearities in dynamic systems with sigmoid functions: advantages and limitations. Nonlinear Dynamics, 111(9), pp. 8545-8569. (doi: 10.1007/s11071-023-08293-1)

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In the industry field, the increasingly stringent requirements of lightweight structures are exposing the ultimately nonlinear nature of mechanical systems. This is extremely true for systems with moving parts and loose fixtures which show piecewise stiffness behaviours. Nevertheless, the numerical solution of systems with ideal piecewise mathematical characteristics is associated with time-consuming procedures and a high computational burden. Smoothing functions can conveniently simplify the mathematical form of such systems, but little research has been carried out to evaluate their effect on the mechanical response of multi-degree-of-freedom systems. To investigate this problem, a slightly damped mechanical two-degree-of-freedom system with soft piecewise constraints is studied via numerical continuation and numerical integration procedures. Sigmoid functions are adopted to approximate the constraints, and the effect of such approximation is explored by comparing the results of the approximate system with the ones of the ideal piecewise counter-part. The numerical results show that the sigmoid functions can correctly catch the very complex dynamics of the proposed system when both the above-mentioned techniques are adopted. Moreover, a reduction in the computational burden, as well as an increase in numerical robustness, is observed in the approximate case.

Item Type:Articles
Additional Information:The authors would like to acknowledge the following grants: RELIANT, Risk EvaLuatIon fAst iNtelligent Tool for COVID19 (No. EP/V036777/1) and GALLANT, Glasgow as a Living Lab Accelerating Novel Transformation (No. NE/W005042/1).
Glasgow Author(s) Enlighten ID:Martinelli, Cristiano and Cammarano, Dr Andrea
Authors: Martinelli, C., Coraddu, A., and Cammarano, A.
College/School:College of Science and Engineering > School of Engineering > Systems Power and Energy
Journal Name:Nonlinear Dynamics
ISSN (Online):1573-269X
Published Online:14 February 2023
Copyright Holders:Copyright © 2023 The Authors
First Published:First published in Nonlinear Dynamics 111(9): 8545-8569
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
311655Risk EvaLuatIon fAst iNtelligent Tool (RELIANT) for COVID19Andrea CammaranoEngineering and Physical Sciences Research Council (EPSRC)EP/V036777/1ENG - Autonomous Systems & Connectivity
313196NERC Strategic Programme CallJaime ToneyNatural Environment Research Council (NERC)NE/W005042/1GES - Geography