A two-mass cantilever beam model for vibration energy harvesting applications

Abstract

While vibration energy harvesting has become a viable means to power wireless sensors, narrow bandwidth is still a hurdle to the practical use of the technology. For conventional piezoelectric or electromagnetic harvesters, having multiple proof masses mounted on a beam is one way to widen the effective bandwidth. This is because the addition of proof masses increases the number of resonant modes within the same frequency range. Based on the assumptions of the Euler-Bernoulli beam theory, this paper presents a continuum-based model for a two-mass cantilever beam. First, the equation of motion is derived from Hamilton's principle. Next, the modal analysis is presented and a steady state solution for harmonic base excitation is derived. The two-mass beam is considered as two serially connected beam segments. In the derivation, emphasis is given to the transition conditions, which would otherwise not appear in the traditional single mass beam model. Experimental validation on a stainless steel beam confirms that the model can accurately predict both natural frequencies and the frequency response of an arbitrary point along the beam. The derivation procedure presented in this paper is applicable to a beam with any number of proof masses. Lastly, it is demonstrated how the model can be applied to a piezoelectric energy harvester.Qing Ou, XiaoQi Chen (senior member of IEEE) and Stefanie Gutschmidt are with the Mechanical Engineering Department,

Low frequency piezoelectric energy harvesting at multi vibration mode shapes

“…A cantilever design with two proof masses has been reported [18] that provides both bending and torsion vibrations and allows harvesting in the two modes of the structure. A two mass beam with masses along the length of a cantilever [19] and a folded beam design with a proof mass [20] have also been presented. Some other designs have been proposed in the literature that have more than one harvesting frequency [21][22][23], however, designing a multi-degree of freedom vibrating structure in MEMS is more challenging due to the microfabrication limitations.…”

Design of serial linkage-type vibration energy harvester with three resonant frequencies

“…It may not be very efficient in a sense that the rest of the cantilevers remains inactive when one cantilever operates at a certain resonant frequency. A different approach to multiresonance frequencies problem was to use two masses on a beam [8], where two resonant frequencies were not located sufficiently close. A 2DOF harvester with one mass attached to a pair of parallel cantilevers and the other to a reverted single cantilever was presented to show that two resonant frequencies can be tuned by varying the proof mass [9].…”

A Piezoelectric Based Energy Harvester with Magnetic Interactions: Modelling and Simulation

“…The capabilities of cantilever piezoelectric energy harvesters to withstand large amount of strain when subjected to mechanical loading and convert mechanical energy in form of vibration into electrical energy make them attractive choices for energy harvesting systems. Most commonly employed methods of transduction from vibration-to-electrical energy are piezoelectric, electromagnetic and electrostatic [1,2]. Irrespective of the transduction mechanism used in designing energy harvester, the challenges that remain unresolved are enhancing the magnitude of the output power and widening the frequency bandwidth of energy harvesters.…”