Mathematical analysis of a wave energy converter model (Q1926442)

This paper studies some mathematical properties of a special type of piecewise linear second-order differential equation with external excitation. This system has been introduced as a simple model for a buoy-type ocean wave converter and is given by \[ \ddot x+2\omega\delta\dot x+\omega x=g(t)\quad\text{for } x\dot x>0, \] and by \[ \ddot x+2\delta\dot x+ x=g(t) \quad \text{for } x\dot x>0, \] where \(g(t)\) is the external force due to the ocean wave. Sufficient conditions are provided for the system to be dissipative and for the existence of periodic solutions. Moreover, an energy balance argument shows that, when \(\omega<1\), the proposed model is more efficient than standard oscillations without mass modulation.