A general nonlinear hysteretic force-deflection relation for a one degree-of-freedom structure is presented. The relation is a continuous, smooth function and describes yielding behavior varying between the limits of the linear and elasto-plastic cases. The steady-state response to sinusoidal excitation of a structure having these properties is investigated, and the resonant amplitude and frequency response curves are obtained. A typical family of these curves is verified by numerical integration of the equation of motion. The equivalent viscous damping factor for the general structure is determined. It is concluded that the relation is sufficiently general to be useful as a model for dynamic behavior of yielding structures. Comparison of dynamic test results to the analytical results can furnish approximations to the dynamic force-deflection relations of many real structures.
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Paul C. Jennings (1964) studied this question.