Nonlinear Analysis and Performance of Electret-Based Microcantilever Energy Harvesters

Abstract

An energy harvester composed of a microcantilever beam with a tip mass and a fixed electrode covered with an electret layer is investigated when subject to an external harmonic base excitation. The tip mass and fixed electrode form a variable capacitor connected to a load resistance. A single-degree-of-freedom model, derived based on Newton’s and Kirshoff’s laws, shows that the tip mass displacement and charge in the variable capacitor are nonlinearly coupled. Analysis of the eigenvalue problem indicates the influence of the electret surface voltage and electrical load resistance on the harvester linear characteristics, namely the harvester coupled frequency and electromechanical damping. Then, the frequency–response curves are obtained numerically for a range of load resistance, electret voltage and base excitation amplitudes. A softening nonlinear effect is observed as a result of decreasing the load resistance and increasing the electret voltage. It is found that there is an optimal electret voltage with the highest harvested electrical power. Below this optimal value, the bandwidth is very small, whereas the bandwidth is large when the electret voltage is above this optimal value. In addition, it is noted that for a certain excitation frequency, the harvested power decreases or increases as a function of electrical load resistance when the coupled frequency is closer to short- or open-circuit frequency, respectively. However, when the coupled frequency is between the short-circuit and open-circuit frequencies, the harvested power has an optimal resistance with the highest power. Increasing the excitation amplitude to raise the harvested power could be accompanied with dynamic pull-in instability and/or softening behavior depending on the electrical load resistance and electret voltage. However, large softening behavior would prevent the pull-in instability, increase the level of the harvested power, and broaden the bandwidth. These observations give a deeper insight into the behavior of such energy harvesters and are of great importance to the designers of electrostatic energy harvesters.

Frequency‐tunable resonant hybrid vibration energy harvester using a piezoelectric cantilever with electret‐based electrostatic coupling

“…The resonant frequency of PEHP is lower than that of the single piezoelectric cantilever due to the electret-based electrostatic coupling. This frequency shift behaviour is attributable to the 'softening' effect brought by the electretoffered electrostatic force coupling, which introduces a non- linear negative stiffness into the vibration system [23,30,34]. According to Equation (11), the strength of the electrostatic force is directly determined by the electric field in the air gap, which is positively correlated with the electret surface potential.…”

Adaptivity of a leaf-inspired wind energy harvester with respect to wind speed and direction

“…Values or ranges of the main dimensional parameters of the basic harvester configuration shown in figure 2 are listed in table 1. It should be mentioned that since, in addition to the tip mass (m tip ), the mass of the leaf stalk (m b ) is also influential on the vibrational behavior, the effective mobile mass of the harvester (m eff, h ) is the sum of m tip and the equivalent mass of the beam springs [49], as given in equation ( 3). Depending on l b , m b and hence m eff, h can be obtained.…”

Ultra-Low Frequency Eccentric Pendulum-Based Electromagnetic Vibrational Energy Harvester

“…According to the working principle of a transducer, the types of vibrational energy harvester can be divided into electrostatic, piezoelectric, and electromagnetic [ 34 ]. Based on the principle of variable capacitance and micro-electro-mechanical system (MEMS) technology, the electrostatic vibration energy harvester usually operates at a frequency higher than 100 Hz [ 35 , 36 , 37 ]. The piezoelectric-based vibrational energy harvester typically introduces a cantilever with piezo film as the transducer, and the working frequency is usually lower than electrostatic types [ 38 , 39 , 40 ].…”