An investigation into resonant frequency of trapezoidal V-shaped cantilever piezoelectric energy harvester

Abstract

have successfully established. On the other hand, for low powered electronics devices, harvesting energy from the ambient vibrations seems to be an ideal solution due to the definite life span and high cost for replacement of the traditional batteries. Three methods are available for vibration energy harvesting; using electrostatic devices, electromagnetic field and utilizing piezoelectric based materials. The performance of piezoelectric vibration energy harvesters for vibration-to-electricity transduction is more often than other methods, because this method has the highest power density. In other words, it can generate the highest electrical power in the same volume. Compared to other structural forms of beams, a cantilever beam can obtain the maximum deformation and strain under the same conditions. The larger deflection leads to more stress, strain, and consequently a higher output voltage and power. Therefore the vast majority of piezoelectric vibration energy harvesting devices use a cantilever beam structure (Anderson and Sexton 2006;Beeby et al. 2006;Erturk and Inman 2011;Priya and Inman 2009). A cantilever-type energy harvester has been intensively studied and a tapered cantilever has been found to be the optimum design (Matova et al. 2013;Siddiqui 2014;Muthalif and Nordin 2015), because it ensures a large constant strain (and a large power output) in the piezoelectric layer.Most of the previous research works focused on designing a linear vibration resonator, in which the maximum system performance can be achieved when the energy harvester is tuned to match its resonance frequency with the external excitation frequency. If the excitation frequency slightly shifts, the performance of the harvester will dramatically decrease. Since in the majority of practical cases, the vibration in the environment is frequency-varying or totally random with the energy distributed in a wide spectrum, how to increase the bandwidth of mechanical Abstract Power supply is a bottle-neck problem of wireless micro-sensors, especially where the replacement of batteries is impossible or inconvenient. Now piezoelectric material is being used as an additional layer in cantilever beams to harvest vibration energy for self-powered sensors. However, the geometry of a piezoelectric cantilever beam will greatly affects its vibration energy harvesting ability. This paper deduces a remarkably precise analytical formula for calculating the fundamental resonant frequency of trapezoidal V-shaped cantilevers using Rayleigh-Ritz method. This analytical formula, which is very convenient for mechanical energy harvester design based on Piezoelectric effect, is then analyzed using MATLAB as well as finite element methods and validated by ABAQUS simulation. This formula raises a new perspective that, among all the trapezoidal V-shaped cantilevers with uniform thickness, the simplest triangular tapered cantilever, can lead to maximum resonant frequency and highest sensitivity and by increasing the ratio of the trapezoidal bases, the sensitivity dec...

Energy Harvesting Research: The Road from Single Source to Multisource

“…Apart from the tuning of the material composition, the rest of the piezoelectric energy harvesting research has focused on the structural design and optimization for different applications. The most popular structures used in piezoelectric energy harvesters include cantilever, stack cymbal configuration, diaphragm configuration, and shear mode configuration . The cantilever structure is suitable for low input force, small acceleration, and mid‐high frequencies (tens of Hz or above), but it allows large amplitude/deformation.…”

Comprehensive Review on Effective Strategies and Key Factors for High Performance Piezoelectric Energy Harvester at Low Frequency

“…With sinusoidal excitation of 2ms -2 at 50Hz, both trapezoidal and reversed trapezoidal beams have greater power density by 24% and 113%, respectively when compared to a rectangular beam. Hosseini and Hamedi [57] reported that the natural frequency of trapezoidal cantilever decreased with increased length. However, this trend was only valid until the length of 70-80 mm.…”

Parameter identification of partially covered piezoelectric cantilever power scavenger based on the coupled distributed parameter solution

“…The main resonance frequency of a simple unimorph cantilever that undergoes undamped free vibration, can be written as [13,14];…”

“…The resonance frequency of the system can be calculated using the theoretical equations developed in previous research works by submitting the substrate in Equation 2 [13,14]. Substrate properties are as follows: Young's Modulus, E = 69 GPa, density of the beam, ρ = 2700 kgm −3 , thickness of the beam, ℎ s = 0.1 cm, width of the beam, w = 5 cm, and length of the beam, L = 15 cm.…”