hysteretic system
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2021 ◽  
Vol 25 (2) ◽  
Author(s):  
Vladimir Cortés Lerin ◽  
Juan Alejandro Vazquez Feijoo ◽  
Rodrigo Arturo Marquet Rivera ◽  
Guillermo Urriolagoitia Sosa ◽  
Beatriz Romero Angles ◽  
...  

2021 ◽  
Author(s):  
L.C. Chen ◽  
Huiying HU ◽  
Shushen Ye

Abstract The dynamical system containing flag-shaped hysteretic behavior is common in practice. In this paper, the stationary response of flag-shaped hysteretic system excited by harmonic excitation as well as Gaussian white noise is determined with the technique of stochastic averaging. The reliability of the presented approach is demonstrated by relevant digital simulation. The stochastic jump under a certain combination of parameters is found. The stochastic P-bifurcation phenomenon, i.e., the disappearance or appearance of bimodal shape of stationary response, occurs concerning to the variation of system’s parameters. Besides, the response of the system exposed to only harmonic excitation or non-resonance case is also examined for comparison, respectively. The numerical results show that the stationary amplitude response displays typical “soft” system behavior, and the deterministic jump may occur under pure harmonic excitation. Moreover, the non-resonance response is always weaker than that of resonant case.


2021 ◽  
Author(s):  
Fan Kong ◽  
Renjie Han ◽  
Yuanjin Zhang

Abstract A method based on statistical linearization is proposed, for determining response of the single-degree-of-freedom (SDOF) hysteretic system endowed with fractional derivatives and subjected to combined periodic and white/colored excitation. The method is developed by decomposing the system response into a combination of a periodic and of a zero-mean stochastic components. In this regard, first, the equation of motion is cast into two sets of coupled fractional-order non-linear differential equations with unknown deterministic and stochastic response components. Next, the harmonic balance method and the statistical linearization for the fractional-order deterministic and stochastic subsystems are used, to obtain the Fourier coefficients of the deterministic component and the variance of the stochastic component, respectively. This yields two sets of coupled non-linear algebraic equations which can be solved by appropriate standared numerical method. Pertinent numerical examples, including both softening and hardening Bouc-Wen hysteretic system endowed with different fractional-orders, are used to demonstrate the applicability and accuracy of the proposed method.


2020 ◽  
Vol 15 ◽  
pp. 55
Author(s):  
Fabio Bagagiolo ◽  
Marta Zoppello

We investigate the controllability of some kinds of driftless affine systems where hysteresis effects are taken into account, both in the realization of the control and in the state evolution. In particular we consider two cases: the one when hysteresis is represented by the so-called play operator, and the one when it is represented by a so-called delayed relay. In the first case we prove that, under some hypotheses, whenever the corresponding non-hysteretic system is controllable, then we can also, at least approximately, control the hysteretic one. This is obtained by some suitably constructed approximations for the inputs in the hysteresis operator. In the second case we prove controllability for a generic hysteretic delayed switching system. Finally, we investigate some possible connections between the two cases.


Metals ◽  
2018 ◽  
Vol 8 (7) ◽  
pp. 562 ◽  
Author(s):  
Kenan Wu ◽  
Hongbai Bai ◽  
Xin Xue ◽  
Tuo Li ◽  
Min Li

A novel coated damping structure for metal rubber (MR) of bellows is designed based on large-size metal rubber sheets. This structure is dynamically tested in the bending direction at normal temperature. According to the test results, a model of the nonlinear elastic restoring force is set up, which describes the dynamic characteristics of the coated damping structure for metal rubber of bellows, and identifies the parameters of the model. The results show that the coated damping structure for metal rubber of bellows has a strong damping energy dissipation ability, its dynamic vibration characteristics are related to the vibration amplitude and frequency, and it is a complex nonlinear hysteretic system with multiple damping components. After identification of the parameters, the model of nonlinear elastic restoring force shows highly accurate results.


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