Design and nonlinear dynamics of piezoelectric energy harvesters: Analytical, computational, and experimental investigation

The modeling and performance of piezoelectric based dynamical systems for the purposes of energy harvesting and control are investigated in this Dissertation. In the first part, two-dimensional beam shapes are investigated as they offer the opportunity to modify the vibration characteristics of the energy harvester for achieving higher power density. The first used shape studied is the elephant structure. The second bending mode shape of this structure is examined and its interaction with the first bending mode is evaluated. A combinatory mode shape created by using mass loading structural modification to lower the second bending modal frequency is found to interact with the first bending mode. This is possible since the first two bending modes do not share common areas of displacement. The combined mode shape is shown to produce the most power of any of the considered mode shape. The second shape proposed is a Zigzag piezoelectric energy harvester that can generate energy at low frequencies and which can be used to operate low-power consumption electronic devices, such as pacemaker. A computational model is developed using ABQUS to determine the exact mode shapes and coupled frequencies of the considered energy harvester. The optimal harvested power from higher order modes is experimentally determined and computationally verified. It is demonstrated that the torsional-dominant mode may decrease the operating frequency by 50% compared to the bending-dominant, mode, allowing the harvester to generate power at lower excitation frequencies.;In the second part of this Dissertation, the concept of controlling dynamical systems through the implementation of piezoelectric energy harvesting absorbers is investigated. Two types of exciations are considered, namely, base and galloping. First, a novel design of piezoelectric beam installed inside an elastically-mounted dynamical system undergoing base excitations is considered. An optimal design is carried out 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. Optimal 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 optimize the 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 an optimization analysis, the optimal 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. Second, an innovative control strategy based on energy hay vesting for efficiently suppressing galloping oscillations is proposed. The novel design enables the harvester of not only alleviating the oscillations of the primary structure but also enhancing the transformed vibrational energy. An analytical model for the coupled nonlinear dynamical system is established by utilizing the Euler-Lagrange principle and implementing the Galerkin discretization. The impacts of the electrical load resistance and tip mass of the energy harvester on the coupled frequency, damping, and the onset speed of instability of the coupled multi-mode system are investigated in details. The results show that there exists an optimal load resistance for each tip mass which maximizes the onset speed of galloping. For control purposes, it is found that there is a well-defined tip mass of the energy harvester at which the coupled system has the highest onset speed of instability and hence the bluff body has the lowest vibration amplitude for all considered load resistances. However, to efficiently harvest energy and control The bluff body, both the tip mass of the energy harvester and electrical load resistance can be accurately determined.;In the last part of the Dissertation, the characteristics and performance of piezoelectric energy harvesters concurrently subjected to galloping and base excitations when using a complex electrical circuit are investigated. The considered energy harvester is composed of a bilayered cantilever beam with a square cylindrical structure at its tip. Euler-Bernoulli beam theory, nonlinear quasi-steady hypothesis. and Galerkin method are used to develop a reduced order model of this system. The electrical circuitry of the harvester consists of a load resistance, a capacitance, and an inductance. The impacts of the electrical components of the harvester's circuitry, the wind speed, and the base excitation frequency and acceleration on the broadband characteristics of the harvester, quenching phenomenon, and appearance of new nonlinear behaviors are deeply investigated and discussed. When both coupled frequencies of ,?lectrical and mechanical types exists and are far from each other, it is shown that the quenching phenomenon is only related to the coupled frequency of mechanical type. On the other hand, for a well-defined choice of the electrical components. the results show that a broadband configuration of the harvester can be designed. It is also indicated that the quenching phenomenon interacts with the appearance of hysteresis regions that depends on the value of the base acceleration and initial conditions.