Hysteresis modelling of mechanical systems at nonstationary vibrations
type: Item
instance of: scholarly article
title: Hysteresis modelling of mechanical systems at nonstationary vibrations
zbMATH Open document ID: 1427.70050
DOI: 10.1155/2018/7102796
author: A. N. Danilin
author: A. D. Shalashilin
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: This paper considers and reviews a number of known phenomenological models, used to describe hysteretic effects of various natures. Such models consider hysteresis system as a ``black box'' with experimentally known input and output, related via formal mathematical dependence to parameters obtained from the best fit to experimental data. In particular, we focus on the broadly used Bouc-Wen and similar phenomenological models. The current paper shows the conditions which the Bouc-Wen model must meet. An alternative mathematical model is suggested where the force and kinematic parameters are related by a first-order differential equation. In contrast to the Bouc-Wen model, the right hand side is a polynomial with two variables representing hysteresis trajectories in the process diagram. This approach ensures correct asymptotic approximation of the solution to the enclosing hysteresis cycle curves. The coefficients in the right side are also determined experimentally from the hysteresis cycle data during stable oscillations. The proposed approach allows us to describe hysteretic trajectory with an arbitrary starting point within the enclosed cycle using only one differential equation. The model is applied to the description of forced vibrations of a low-frequency pendulum damper.
Mathematics Subject Classification ID: 70K25
Mathematics Subject Classification ID: 34C55
zbMATH DE Number: 7019396
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/7102796
OpenAlex ID: W2792267274
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Wikidata QID: Q130184188
description: scientific article; zbMATH DE number 7019396