Periodic Response of Yielding Oscillators

A new method is employed to obtain the response of a general yielding oscillator to harmonic excitation. This method can be applied to a wide range of hysteretic systems, once the skeleton curve and the loop is defined. In this paper, responses are obtained for four different models, describing the hysteretic behavior of physical system. The analytical expressions for the frequency response curves and the frequency shift at peak responses are obtained. They are extremely simple, even for a general curved hysteresis loop. Results are compared with the numerical solutions and the findings of earlier investigators. Peak responses turn out to be exactly the same as that obtained by earlier researchers, but the frequency shift shows some difference. For a bilinear system, the frequency shift at peak response is a function of load level only, and the post yielding slope determines only the lower bound on the frequency shift. Also the frequency response curves are not single valued, contrary to the earlier findings, specially corresponding to lower peak responses.