Approximating piecewise nonlinearities in dynamic systems with sigmoid functions: advantages and limitations
Approximating piecewise nonlinearities in dynamic systems with sigmoid functions: advantages and limitations
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.
Basins of attraction, Non-smooth systems, Nonlinear dynamics, Numerical continuation, Period doubling isolated solutions, Piecewise stiffness, Sigmoid functions
8545-8569
Martinelli, C.
33b061e6-93a5-42a6-a865-03beaf2ef4ab
Coraddu, A.
eb41a72b-88f2-43f2-b685-ed948f2aa818
Cammarano, A.
c0c85f55-3dfc-4b97-9b79-e2554406a12b
2023
Martinelli, C.
33b061e6-93a5-42a6-a865-03beaf2ef4ab
Coraddu, A.
eb41a72b-88f2-43f2-b685-ed948f2aa818
Cammarano, A.
c0c85f55-3dfc-4b97-9b79-e2554406a12b
Martinelli, C., Coraddu, A. and Cammarano, A.
(2023)
Approximating piecewise nonlinearities in dynamic systems with sigmoid functions: advantages and limitations.
Nonlinear Dynamics, 111 (9), .
(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.
Text
s11071-023-08293-1
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Accepted/In Press date: 16 January 2023
e-pub ahead of print date: 14 February 2023
Published date: 2023
Keywords:
Basins of attraction, Non-smooth systems, Nonlinear dynamics, Numerical continuation, Period doubling isolated solutions, Piecewise stiffness, Sigmoid functions
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Local EPrints ID: 490804
URI: http://eprints.soton.ac.uk/id/eprint/490804
ISSN: 0924-090X
PURE UUID: 130fdc03-9924-49c1-9d8d-4385d2e0ee1b
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Date deposited: 06 Jun 2024 16:59
Last modified: 21 May 2026 02:10
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Author:
C. Martinelli
Author:
A. Coraddu
Author:
A. Cammarano
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