An Exact Analytical Solution to Exponentially Tapered Piezoelectric Energy Harvester

Abstract

It has been proven that tapering the piezoelectric beam through its length optimizes the power extracted from vibration based energy harvesting. This phenomenon has been investigated by some researchers using semianalytical, finite element and experimental methods. In this paper, an exact analytical solution is presented to calculate the power generated from vibration of exponentially tapered unimorph and bimorph with series and parallel connections. The mass normalized mode shapes of the exponentially tapered piezoelectric beam with tip mass are implemented to transfer the proposed electromechanical coupled equations into modal coordinates. The steady states harmonic solution results are verified both numerically and experimentally. Results show that there exist values for tapering parameter and electric resistance in a way that the output power per mass of the energy harvester will be maximized. Moreover it is concluded that the electric resistance must be higher than a specified value for gaining more power by tapering the beam.

Performance enhancement of cantilever piezoelectric energy harvesters by sizing analysis

“…As the second part of validation, the output voltage of one non-uniform PEH is compared with the literature [10]. They assumed that the width of the beam is varying exponentially through the length by b x ð Þ ¼ b 0 e Àcx .…”

“…Regarding the development of MEMS power generators, fixed or narrow operation frequency range and low power output are the most important challenges [10]. To address the issue, researchers always have been attempting to reach to higher performance using different practical methods such as modification of shape, size, material properties, and damping [11][12][13][14][15].…”

“…The effectiveness of tapered beam configuration can also be seen in other researches [11,[33][34][35]. Changing the thickness of the substrate layer or mounting a tip mass are two practical methods which have been exploited to change the resonance frequency of the cantilever energy harvesters [10]. Other studies were carried out to improve the output power and decrease the fundamental frequency through the application of a parallel or series array of piezoelectric energy harvesters (PEHs) [26,36].…”

Performance of non-uniform functionally graded piezoelectric energy harvester beams

“…In the second part of the validation, the output voltage of one non-uniform PEH is analyzed (Salmani et al, 2015). It was assumed that the width of the beam is varying exponentially through the length by b ( x ) = b 0 e − cx .…”

High-output piezoelectric energy harvester using tapered beam with cavity

“…The structures for harvesting energy using piezoelectric consists of additional components such as mass, additional beams and altering the shape to enhance the output voltage from the energy harvester (Matova et al, 2013; Zhu et al, 2010). The output voltage obtained from vibration of exponentially tapered piezoelectric beam with series and parallel connections and also with tip mass is analysed analytically by Salmani et al (2015). A piezoelectric air-spaced cantilever was designed and demonstrated by Wang and Xu (2007).…”