Approximating piecewise nonlinearities in dynamic systems with sigmoid functions

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

Martinelli, Cristiano (University of Strathclyde)
Coraddu, A. (TU Delft Ship Design, Production and Operations)
Cammarano, Andrea (University of Glasgow)

2023

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

http://resolver.tudelft.nl/uuid:850096e5-bdf2-4215-8969-9f1c53928b50

https://doi.org/10.1007/s11071-023-08293-1

0924-090X

Nonlinear Dynamics: an international journal of nonlinear dynamics and chaos in engineering systems, 111 (9), 8545-8569

Institutional Repository

journal article

© 2023 Cristiano Martinelli, A. Coraddu, Andrea Cammarano