Analysis on steady-state asymmetric impact vibration of continuous system with hysteresis loop characteristic

An analytical method for asymmetrical impact vibration of a beam excited periodically is investigated. As the analytical model of the beam, a cantilever is used. The cantilever collides with a clamped steel stop once in one period of its vibration at arbitral point of a span. In order to consider energy loss in a collision and duration of collision, relation between the force of restitution and the displacement response is modeled as triangular hysteresis loop characteristic. The Fourier series method is applied and approximate solutions of the steady-state responses are obtained. Obtained results are verified experimentally. The analytical results agree well with the experimental results. Applying variation equation, the infinitesimal stabilities are analyzed. It is found that the experimental results are observed at the stable regions of the analytical method.