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

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Journal of Vibration and Shock ›› 2018, Vol. 37 ›› Issue (10) : 57-62.

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

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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.

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hysteresis nonlinear / Bouc-Wen model / cantilever / IHB method / arc-length method

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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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