Thickness-variable composite beams for vibration energy harvesting

Abstract

Researchers have recently focused on improving the efficiency of piezoelectric energy harvesters by redesigning their substrate beams. Two approaches have been explored, including changing the shape of the cross-section area, i.e., width variation, and changing the thickness of cantilever beams. The width changing approach suffers from the deduction of output power from the piezoelectric elements of the trimmed-off regions, while performance deterioration does not occur in the thickness-variable approach. The benefit of thickness-variable beams on energy harvesting has been analyzed theoretically, but its detailed experimental study is still absent. In this study, we for the first time fabricate a thickness-variable harvester based on the Garolite FR-4 epoxy laminate, and validate the superiority of the variable thickness beam on the harvester performance enhancement. A theoretical model is developed based on the Euler-Bernoulli beam theory and numerically solved via the Rayleigh-Ritz method. We compare the thickness-variable composite beam configuration with a conventional uniform-thickness counterpart and unveil the beneficial effect of evenly-distributed strain on performance enhancement. Experiments indicate that the thickness-variable method increases on the energy harvester efficiency by 78%.

Introduction

Advances in low power electronic devices open up the possibility of developing self-powered systems by scavenging ambient energy from the environment. Piezoelectric energy harvesters have been used in a wide range of scenarios, such as structural health monitoring systems, smart wireless devices [1], [2], [3]. To enhance the power output of generators, the research communities have resorted to various approaches including nonlinear bandwidth broadening techniques [4], [5], [6], [7], [8], [9], [10], [11], multilayer piezoelectric stacks [12], [13], [14], [15], [16] and force amplification mechanism [17], [18]. Despite the distinctive advantages of these structures, the cantilever-based harvesters are still extensively used and receive the most attention due to the ease of fabrication, small size, light in weight, low working loading conditions and ease application [19], [20].

To further improve the performance of cantilever-typed energy harvesters, efforts have been dedicated to redesigning the cross-section area or the thickness. For example, Shebeeb and Salleh [21], via the finite element method (FEM), analyzed the cantilever beam with triangular, rectangular and trapezoidal cross-section and calculated the output power for each beam. In their work, only the substrate layer was considered. Other works focused on analytical modeling and experiments. Goldschmidtboeing and Woias [22] used the Rayleigh-Ritz method to study different beam shapes, and the analytical results were validated by experiments. Ben Ayed et al. [23] exploited a one-mode Galerkin approach to derive the reduced-order model. Salmani and Rahimi [24] formulated the behavior of nonlinear piezoelectric energy harvester with exponentially tapering width. It showed that the structure improved voltage per mass at a high exciting acceleration amplitude. Baker et al. [25] experimentally investigated output power by comparing the cantilever beam designs with rectangular and trapezoidal shapes. Similar works can be found in the literature [26], [27], [28], [29], [30]. Table 1 summarizes the main features of some variable cross-section area energy harvesters. The power amplification ratio is obtained by comparing the variable cross-section energy harvesters with the uniform counterparts. It can be found that both analytical models and experiments were utilized in optimizing the cross-section.

But one should note that piezoelectric materials, especially piezoelectric ceramics, are extremely brittle. The cutting processes would significantly increase the costs [25]. In addition, the piezoelectric materials would lose the output power in the trimmed-off regions. Thus, some researchers have explored the effect of variable thickness of the substrate layer on the conversion efficiency. Paquin and St-Amant [31] investigated the optimum slope angle of a tapered cantilever beam for the best performance by semi-analytical mechanical model. It reported that the tapered energy harvester could generate 3.6 times higher power output than the uniform thickness beam. The result was compared with a FEM simulation. Later, Xie et al. [32] established a finite differential theoretical model to study the effect of taper ratios in width and thickness of the energy harvester. They concluded that 70 times higher power output could be achieved. Keshmiri et al. [33] studied functionally graded material piezoelectric energy harvester with a nonlinearly tapered thickness using a theoretical model. They found that the design is capable of generating 19.76 times as much voltage as its uniform counterpart. A similar study was implemented by Raju et al. [34], in which they used the Euler-Bernoulli beam theory to develop an analytical model and proved that the voltage was increased by up to 126.6%. Recently, Keshmiri and Wu [35] designed wideband piezoelectric energy harvesters by combining an array of non-uniform thickness cantilever bimorphs. Based on the theoretical optimization, they pointed out the design can obtain around five times larger peak voltage output compared with the uniform thickness one. Other forms of change in thickness included elliptical [36], parabolic, hyperbolic [37] and tapered profiles. Table 2 lists the main features of previously reported thickness-variable harvesters.

However, as can be seen in Table 2, the main research methods in the literature on optimizing the thickness are numerical simulation and analytical modeling. Few have conducted an experimental study and the predicted power amplification ratio has a large difference. In addition, these studies predicted the electrical responses of the harvesters but were lack of the further explanation of the power reinforcement mechanisms. In this study, we will fill the gap between theoretical analysis and experiments. The prototypes with a variable thickness are fabricated for quantitatively characterizing its performance enhancement effect, which is further explained by theoretical models.

In this paper, the authors numerically and experimentally investigate a unimorph cantilever beam with a variable thickness. PZT-5H and Garolite FR-4 are used as piezoelectric and substrate layer, respectively. Section 2 is dedicated to developing the theoretical model with a varying thickness and validating it by the FEM simulation. Section 3 presents the experimental platform. Section 4 details the results derived from theoretical analysis and the experiments and unveil beneficial effect of evenly-distributed strain on performance enhancement. Finally, the conclusion is given in Section 5.