Influence of small harmonic terms on eigenvalues of monodromy matrix of piecewise-linear oscillators

Wolf, Hinko; Banić, Dubravko; Sušić, Aleksandar

doi:10.1007/s11012-008-9112-z

Cited by 1 publication

(1 citation statement)

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“…However, the author did not evaluate the extension of the error caused by the smoothing function, focusing the numerical observations on chaotic responses. Wolf et al [47,48] studied the dynamical stability of piecewise systems; in particular, they analysed the effect of smoothing functions on the stability of an SDOF mechanical system with free-play gaps when the Harmonic Balance Method is utilised [44]. They demonstrated that the smoothing functions introduce only limited inaccuracies in the computation of the system stability and that the effect of the number of harmonics is more important than the effect of the smoothing approximation.…”

Section: Introductionmentioning

confidence: 99%

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

2023

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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.

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Section: Introductionmentioning

confidence: 99%