Control of base-excited dynamical systems through piezoelectric energy harvesting absorber

Abstract

The spring-mass absorber usually offers a good control to dynamical systems under direct base excitations for a specific value of the excitation frequency. As the vibrational energy of a primary dynamical system is transferred to the absorber, it gets dissipated. In this study, this energy is no longer dissipated but converted to available electrical power by designing efficient energy harvesters. A novel design of a piezoelectric beam installed inside an elastically-mounted dynamical system undergoing base excitations is considered. A design is carried out in order to determine the properties and dimensions of the energy harvester with the constraint of simultaneously decreasing the oscillating amplitudes of the primary dynamical system and increasing the harvested power of the energy harvesting absorber. An analytical model for the coupled system is constructed using Euler–Lagrange principle and Galerkin discretization. Different strategies for controlling the primary structure displacement and enhancing the harvested power as functions of the electrical load resistance and thickness of the beam substrate are performed. The linear polynomial approximation of the system’s key parameters as a function of the beam’s substrate thickness is first carried out. Then, the gradient method is applied to determine the adequate values of the electrical load resistance and thickness of the substrate under the constraints of minimizing the amplitudes of the primary structure or maximizing the levels of the harvested power. After that, an iterative strategy is considered in order to simultaneously minimize the amplitudes of the primary structure and maximize the levels of the harvested power as functions of the thickness of the substrate and electrical load resistance. In addition to harmonic excitations, the coupled system subjected to a white noise is explored. Through this analysis, the load resistance and thickness of the substrate of the piezoelectric energy harvester are determined. It is shown that, in addition to efficiently control the oscillating amplitudes of the primary structure, broadband resonance regions can take place and hence high levels of the harvested power are obtained.