基于分数阶微分的金属橡胶迟滞非线性动力学模型

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Abstract The stress-strain characteristic of metal rubber components appears as a nonlinear hysteretic curve.Most of the existing dynamic models for metal rubber are described by multi-parameter and piecewise functions, increasing the complexity of the system.Making use of the fractional-order derivative which has been applied to the description of the memory characteristics of various materials and processes, a viscoelastic constitutive model for metal rubber with the fractional-order derivative was established through analyzing the composition of the elastic restoring force and the damping force of metal rubber.On this basis, a nonlinear dynamic system model for metal rubber was founded.The restoring force of a typical metal rubber vibration isolation system was analyzed through sinusoidal displacement loading experiments under various excitation amplitudes and frequencies.All the parameters of the model were identified by the curve fitting of the experimental data with the genetic algorithm.The functional relationships between the parameters of the system model and the amplitude and frequency were derived by a series of analysis.The results show that the nonlinear dynamic system model for metal rubber with a fractional order differential item can be described as continuous mathematical expressions，which can reflect the full metal rubber nonlinear system dynamic performance.The model involves less parameters and has a simpler structure compared to other existing metal rubber dynamics system models.The results provide a new way to the study of metal rubber dynamics systems.

Key words： metal rubber fractional-order derivative nonlinear dynamics hysteretic characteristic

Received: 28 February 2019 Published: 15 July 2020

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	Articles by authors
	CHANG Yujian1
	TIAN Wowo1
	CHEN Enli2
	SHEN Yongjun2
	XING Wuce2

Cite this article:

CHANG Yujian1,TIAN Wowo1,CHEN Enli2, et al. Dynamic model for the nonlinear hysteresis of metal rubber based on the fractional-order derivative[J]. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(14): 233-241.

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http://jvs.sjtu.edu.cn/EN/ OR http://jvs.sjtu.edu.cn/EN/Y2020/V39/I14/233

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