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)

Abstract

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).
• Status: Published
• Refereed: Yes
• 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
• Publisher: Springer
• ISSN: 0924-090X
• 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

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
311655		Risk EvaLuatIon fAst iNtelligent Tool (RELIANT) for COVID19	Andrea Cammarano	Engineering and Physical Sciences Research Council (EPSRC)	EP/V036777/1	ENG - Autonomous Systems & Connectivity
313196		NERC Strategic Programme Call	Jaime Toney	Natural Environment Research Council (NERC)	NE/W005042/1	GES - Geography