The Dynamic Response of Bilinear Hysteretic Systems

Citation

Iwan, Wilfred Dean (1961) The Dynamic Response of Bilinear Hysteretic Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Y32J-KT73. https://resolver.caltech.edu/CaltechETD:etd-10052004-162528

Abstract

A study is made of the dynamic response of one and two degree of freedom systems having a bilinear hysteretic restoring force. In the case of the one degree of freedom system exact steady state solutions are obtained for both square wave and trigonometric excitation. It is thereby shown that the system exhibits a soft type resonance and that there exists a critical level of excitation above which the system displays unbounded resonance. An approximate steady state theory for the one degree of freedom system is investigated and on the basis of this theory it is found that the system is stable and possesses a single locus of vertical tangency. The results of the exact and approximate steady state theories are supplemented by electric analog studies of both the harmonic and ultraharmonic response. The response of the one degree of freedom system to transient excitation of finite duration is also examined and it is noted that certain rather general conclusions may be made about the final state of the system without reference to the specific time history of the excitation. A first order approximate theory for the steady state response of the two degree of freedom system is formulated and it is shown that there are two critical levels of excitation for unbounded resonance. The existence of loci of vertical tangency is demonstrated and the stability problem is treated in limiting cases. Direct numerical integration of the equations of motion is carried out for a number of specific cases as a check of the approximate theory.

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