Modelling of hysteresis using Masing–Bouc-Wen’s framework and search of conditions for the chaotic responses

Chaotic vibrations in a damage oscillator with crack closure effect

“…The Melnikov method can be used to show the possible occurrence of chaos, for certain range of parameters of the system. We mention the application of the Melnikov method to nonsmooth dynamics [Awrejcewicz and Lamarque 2003;Awrejcewicz and Holicke 2007;Kukučka 2007]. As shown by Kukučka [2007], the mathematical background of the Melnikov method applied to nonsmooth systems is very recent and complex.…”

“…Coupling with geometrical nonlinearities also leads to chaotic motion [Poddar et al 1988]. Without being exhaustive, let us mention also that chaos may appear in a Bouc-Wen hysteretic oscillator [Lacarbonara and Vestroni 2003;Awrejcewicz et al 2008]. It has to be pointed out that these material sources of nonlinearities are mainly investigated from a theoretical point of view, and very few papers have been devoted to the experimental evidence of chaos in these nonsmooth oscillators.…”

“…In the case of seismic analysis, knowledge of the basic dynamics of inelastic systems (plastic or damageable systems) is among the main objectives. This is however quite an open issue because these models are nonsmooth dissipative systems and very few results have been established in this particular case [Wiercigroch 2000;Awrejcewicz and Lamarque 2003]. Although concrete structures are inelastic multiple-degree of freedom (DOF) systems, their dynamics are so complex that there is still room for use of a simple approach, based on single-DOF inelastic oscillators, in order to investigate and to illustrate their basic characteristics.…”

A phenomenological stress–strain model for wrought magnesium alloys under elastoplastic strain-controlled variable amplitude loading

“…For this comparison, completely reversed strain controlled constant amplitude tests on the alloy AZ31 were used in [23] and similar tests on the alloys AE42, AZ31, and AZ80 were used in [34]. Phenomenological formulations to describe the shape of non-symmetrical or sigmoidal shaped material behavior already exist [38,39]. The model in [38] can be used for quasi-static loading without unloading.…”

“…It does not contain equations and conditions, necessary for modelling hysteresis loops, especially for asymmetric hysteresis loops. In [39], a method to fit sigmoidal shaped hysteresis loops by the use of a hyperbolic tangent function is presented. This phenomenological model is able to calculate symmetric hysteresis loops.…”