Parametric resonance of a single-degree-of-freedom system with double bilinear hysteresis

A simple pendulum with a hinge of double bilinear hysteretic restraining moment-rotation characteristic under parametric excitation is studied. In contrast with a linear system with viscous damping, a double bilinear hysteretic system leads, in general, to finite response under parametric resonance. The response curves and the conditions under which unbounded response results are given. Further, it is shown that unlike the bilinear hysteretic system, a double bilinear hysteretic system may be shock excited into parametric resonance even when the exciting frequency is outside the parametrically resonant frequency range.