KEYWORDS: Magnetism, Beam shaping, 3D modeling, Energy harvesting, Finite element methods, Energy conversion efficiency, Amplifiers, Transducers, Electromagnetism, Resonators
This paper describes the finite element modeling and experimental testing of a magnetic T-shaped piezoelectric energy harvester that activates the internal resonance phenomena to increase voltage output and frequency bandwidth. The harvester consists of two magnets and two coupled beams, a cantilever piezoelectric beam attached to a clamped-clamped beam. A finite-element model is used to obtain the global mode shapes and natural frequencies of the system. We controlled the distance between the two magnets to achieve a nonlinear phenomenon of internal resonance of the structure, where the 2:1 ratio is satisfied between the modal natural frequencies. The T-shaped structure is combined with the magnetic nonlinearity such that a large, distinct internal resonance can occur at much lower excitation levels compared to a T-shaped structure without magnetic nonlinearity. Presented experimental results validate the benefits of the T-shaped structure nonlinearity when combined with a magnetic nonlinearity to achieve higher bandwidth and large responses, which can improve the energy conversion efficiency of the vibration energy harvester.
Parametric excitation has been investigated for several years as an effective way to drive a structure parametrically into large distinctive responses. However, parametric resonance requires a minimum threshold of excitation to be triggered. To reduce the threshold, we propose a two-degree-of-freedom vibration system. This system consists of two perpendicular beams each with a tip magnet placed so the same poles face each other. The repulsive magnetic force couples the motion of the two beams. By decreasing the distance between the magnets, the threshold value for parametric excitation decreases. In addition, the repulsive magnetic force decreases the first resonance frequency of the vertical beam and thus its principal parametric resonance. Lowering the threshold excitation and parametric resonance frequency are two unique properties that make the device ideal for energy harvesting at low frequencies.
Converting ambient mechanical energy to electricity, vibration energy harvesting, enables powering of the low-power remote sensors. Nonlinear energy harvesters have the advantage of a wider frequency spectrum compared to linear resonators making them more efficient in scavenging the broadband frequency of ambient vibrations. To increase the output power of the nonlinear resonators, we propose an energy harvester composed of a cantilever piezoelectric beam carrying a movable magnet facing a fixed magnet at a distance. The movable magnet on the beam is attached to a spring at the base of the beam. The spring-magnet system on the cantilever beam creates the variable double well potential function. The spring attached to the magnet is in its compressed position when the beam is not deflected, as the beam oscillates, the spring energy gradually releases and further increases the amplitude of vibration. To describe the motion of the cantilever beam, we obtained two coupled partial differential equations by assuming the cantilever beam as Euler-Bernoulli beam considering the effect of the moving magnet. Method of multiple scales is used to solve the coupled equations. The cantilever beam with the two magnets is a bi-stable system. Making one magnet movable can create internal resonance that is explored as a mechanism to increase the frequency bandwidth. The effect of system parameters on the frequency bandwidth of the resonator is investigated through numerical solutions. This study benefits vibration energy harvesting to achieve a higher performance when excited by the wideband ambient vibrations.
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