IHB法在多自由度Bouc-Wen滞回非线性系统响应特性研究中的应用

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (10) : 57-62.

论文

赵倩1，刘子良2，姚红良2，闻邦椿2

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Application of the IHB method to study the response characteristics of multi DOF systems with Bouc Wen hysteretic nonlinearity

ZHAO Qian1, LIU Zi-liang2, YAO Hong-liang2, WEN Bang-chun2

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摘要

工程中常用Bouc-Wen模型来描述具有滞回特性的振动系统，此类系统是一种多值性的非解析系统，其动力学理论分析比较困难。由于Bouc-Wen滞回模型的微分形式，一般采用数值方法进行积分求解，但对于多自由度系统来说求解速度非常慢，且难以求得不稳定解。故提出将滞回力引入为一个增加的自由度，重新建立振动系统的微分方程，将增量谐波平衡(IHB)法推广至求解该类含Bouc-Wen模型的多自由度滞回非线性系统，并引入弧长法解决由迟滞非线性引起的跳跃和多映射现象。利用该法分析了一些滞回系统的响应特性，通过与数值方法进行精度和效率对比，体现了该方法的优越性。

Abstract

The BoucWen model is commonly used to depict hysteretic nonlinear vibration systems in engineering, but the dynamic analysis of such system is difficult due to its multivalued and nonanalytic properties. Numerical integration methods are usually utilized in view of the differential form of BoucWen model; however, it is timeconsuming when dealing with multidegreeoffreedom (multiDOF) systems and even cannot obtain instable solutions. Therefore, the way of considering the hysteretic force as an additional DOF and introducing it into the original system was proposed, thereby the vibration differential equation of the system was rebuilt. Then, the incremental harmonic balance (IHB) method was extended to the study on the response characteristics of such multiDOF hysteresis nonlinear systems with BoucWen model, and the arclength method was also introduced to settle the problems of jump and multimapping caused by hysteretic nonlinearity. Applying the present method, some response characteristics of the hysteretic system were analyzed. The efficiency and precision was verified by comparing with the Newmarkβ numerical integration.

导出引用

赵倩1，刘子良2，姚红良2，闻邦椿2. IHB法在多自由度Bouc-Wen滞回非线性系统响应特性研究中的应用[J]. 振动与冲击, 2018, 37(10): 57-62

ZHAO Qian1, LIU Zi-liang2, YAO Hong-liang2, WEN Bang-chun2. Application of the IHB method to study the response characteristics of multi DOF systems with Bouc Wen hysteretic nonlinearity[J]. Journal of Vibration and Shock, 2018, 37(10): 57-62

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