Abstract
In prior work (Biswas & Chatterjee 2014 Proc. R. Soc. A 470, 20130817 (doi:10.1098/rspa.2013.0817)), we developed a six-state hysteresis model from a high-dimensional frictional system. Here, we use a more intuitively appealing frictional system that resembles one studied earlier by Iwan. The basis functions now have simple analytical description. The number of states required decreases further, from six to the theoretical minimum of two. The number of fitted parameters is reduced by an order of magnitude, to just six. An explicit and faster numerical solution method is developed. Parameter fitting to match different specified hysteresis loops is demonstrated. In summary, a new two-state model of hysteresis is presented that is ready for practical implementation. Essential Matlab code is provided.
Highlights
In this paper, we follow up on our recent work on lowdimensional modelling of frictional hysteresis [1]
A 470, 20130817), we developed a six-state hysteresis model from a high-dimensional frictional system
We show results of fitting the hysteresis model to some arbitrary input data
Summary
We follow up on our recent work on lowdimensional modelling of frictional hysteresis [1]. The net result is a two-state hysteresis model that captures minor loops under small reversals within larger load paths and is ready for practical numerical implementation (simple Matlab code is provided). The famous Bouc–Wen model ([9,10]; see [11]) is one-dimensional but fails to form minor loops under small reversals within larger load paths. With this background, we recently studied [1] a frictional hysteretic system given by μ sgn(x) + Kx = bf (t),. As far as we know, the two-state model developed here has no parallel in the literature
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