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Recently, piezoelectric cantilevered beams have received considerable attention for vibration-to-electric energy conversion. Generally, researchers have investigated a classical piezoelectric cantilever beam with or without a tip mass. In this paper, we propose the use of a unimorph cantilever beam undergoing bending-torsion vibrations as a new piezoelectric energy harvester. The proposed design consists of a single piezoelectric layer and a couple of asymmetric tip masses; the latter convert part of the base excitation force into a torsion moment. This structure can be tuned to be a broader band energy harvester by adjusting the first two global natural frequencies to be relatively close to each other. We develop a distributed-parameter model of the harvester by using the Euler-beam theory and Hamilton's principle, thereby obtaining the governing equations of motion and associated boundary conditions. Then, we calculate the exact eigenvalues and associated mode shapes and validate them with a finite element (FE) model. We use these mode shapes in a Galerkin procedure to develop a reduced-order model of the harvester, which we use in turn to obtain closed-form expressions for the displacement, twisting angle, voltage output, and harvested electrical power. These expressions are used to conduct a parametric study for the dynamics of the system to determine the appropriate set of geometric properties that maximizes the harvested electrical power. The results show that, as the asymmetry is increased, the harvester's performance improves. We found a 30% increase in the harvested power with this design compared to the case of beams undergoing bending only. We also show that the locations of the two masses can be chosen to bring the lowest two global natural frequencies closer to each other, thereby allowing the harvesting of electrical power from multi-frequency excitations.

A model for harvesting energy from galloping oscillations of a bar with an equilateral triangle cross-section attached to two cantilever beams is presented. The energy is harvested by attaching piezoelectric sheets to cantilever beams holding the bar. The derived nonlinear distributed-parameter model is validated with previous experimental results. The quasi-steady approximation is used to model the aerodynamic loads. The power levels that can be generated from these vibrations, and the variations of these levels with the load resistance and wind speed, are determined. Linear analysis is performed to validate the onset of galloping speed with experimental measurements. The effects of the electrical load resistance on the onset of galloping are then investigated. The results show that the electrical load resistance affects the onset speed of galloping. A nonlinear analysis is also performed to determine the effects of the electrical load resistance and the nonlinear torsional spring on the level of the harvested power. The results show that maximum levels of harvested power are accompanied by minimum transverse displacement amplitudes. It is also demonstrated that there is an optimum load resistance that maximizes the level of the harvested power.

This work investigates the influence of structural and aerodynamic nonlinearities on the dynamic behavior of a piezoaeroelastic system. The system is composed of a rigid airfoil supported by nonlinear torsional and flexural springs in the pitch and plunge motions, respectively, with a piezoelectric coupling attached to the plunge degree of freedom. The analysis shows that the effect of the electrical load resistance on the flutter speed is negligible in comparison to the effects of the linear spring coefficients. The effects of aerodynamic nonlinearities and nonlinear plunge and pitch spring coefficients on the system's stability near the bifurcation are determined from the nonlinear normal form. This is useful to characterize the effects of different parameters on the system's output and ensure that subcritical or "catastrophic" bifurcation does not take place. Numerical solutions of the coupled equations for two different configurations are then performed to determine the effects of varying the load resistance and the nonlinear spring coefficients on the limit-cycle oscillations (LCO) in the pitch and plunge motions, the voltage output and the harvested power.

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The concept of harvesting energy from transverse galloping oscillations of a bluff body with different cross-section geometries is investigated. The energy is harvested by attaching a piezoelectric transducer to the transverse degree of freedom of the body. The power levels that can be generated from these vibrations and the variations of these levels with the load resistance, cross-section geometry, and freestream velocity are determined. A representative model that accounts for the transverse displacement of the bluff body and harvested voltage is presented. The quasi-steady approximation is used to model the aerodynamic loads. A linear analysis is performed to determine the effects of the electrical load resistance and the cross-section geometry on the onset of galloping, which is due to a Hopf bifurcation. The normal form of this bifurcation is derived to determine the type (supercritical or subcritical) of the instability and to characterize the effects of the linear and nonlinear parameters on the level of harvested power near the bifurcation. The results show that the electrical load resistance and the cross-section geometry affect the onset speed of galloping. The results also show that the maximum levels of harvested power are accompanied with minimum transverse displacement amplitudes for all considered (square, D, and triangular) cross-section geometries, which points to the need for performing a coupled analysis of the system.

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