Electromechanical Modeling of the Low-Frequency Zigzag Micro-Energy Harvester

Abstract

An analytical electromechanical model is proposed to predict the deflection, voltage, and the power output of a proposed low-frequency micro-harvesting structure. The high natural frequencies of the existing designs of micro-scale vibrational energy harvesters are serious drawbacks. A zigzag design is proposed to overcome this limitation. First, the natural frequencies and the mode shapes of the zigzag structure are calculated. The piezoelectric direct and reverse effect equations, together with the electrical equations, are used to relate the voltage output of the structure to the base vibrations magnitude and frequency. The closed-form solution of the continuous electromechanical vibrations gives the power output as a function of base acceleration spectrum. The usefulness of the design is proved by the significant increase of the power output from the same base accelerations, providing a method of designing a micro-scale harvester with low natural frequency. The optimal mechanical and electrical conditions for power generation are investigated through the case studies.

Bimorph piezoelectric vibration energy harvester with flexible 3D meshed-core structure for low frequency vibration

“…The elastic layer is formed of a thick-film photoresist and has a 3D meshed-core structure to lower resonance frequency, as shown in Figure 1. The conventional studies to lower resonance frequency use the methods as follows: (1) low Young’s modulus of polymer materials [7], (2) heavy weight of the proof mass [13], (3) long entire length of the cantilever (from the fixed end to the free end) [8,9,16]. The simplest approach is to use heavy proof mass; however, the mass and volume of the whole device will easily increase and it is not preferable for practical applications.

10.1080/14686996.2018.1508985-F0001Figure 1.Schematic of the proposed PVEH with 3D meshed-core structure (10 mm × 21 mm × 280 μm).

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“…(2) The meshed-core structure can be combined with previously studied structures and shapes such as ‘2D structures (e.g. meandered or spiral structure [9,16])’ for reducing the resonance frequency, and 2D shapes (e.g. trapezoid, triangle [20,21]) for improving power generation.…”

“…They are inefficient at low-frequency (under 20 Hz) or low-acceleration (0.1 to 1 G) conditions which relate to various human activities, bridge vibration, and house appliances. Some studied harvesters can operate at low frequencies, but they are either too large to be wearable, or their electrical output is insufficient for powering typical consumption devices [7–9]. …”

Distributed-Parameter Modeling of Energy Harvesting Structures with Discontinuities

“…Changing the number and location of piezoelectric patches or layers along the beam can improve coupling and shift the natural frequency of the device (Guyomar et al, 2005;Wu et al, 2009). Multi-beam structures can compact the design by folding it in on itself while retaining a similar natural frequency to the original, straight configuration (Karami & Inman, 2011;Erturk et al, 2009). A nonlinear technique called "frequency up-conversion" also shows promise to boost power at frequencies more than an order of magnitude below resonance (Murray & Rastegar, 2009;Tieck et al, 2006;Wickenheiser & Garcia, 2010b).…”

“…This method is derived from the classical transfer matrix method (TMM) for multi-component structures and trusses (Pestel & Leckie, 1963) combined with an existing model for constant cross section, Euler-Bernoulli beam energy harvesters (Wickenheiser & Garcia, 2010c). A variation of this technique is employed by (Karami & Inman, 2011) to find the natural frequencies and mode shapes of a zigzag structure; however, their formulation is specific to 180° bends between segments. The TMM has been shown to reduce to the classical solutions (e.g.…”