Optimized Mechanical Performance of Cantilevered Vibration Energy Harvesters Using a Modal Approach

2014 ◽  
Author(s):  
X. Xiong ◽  
S. O. Oyadiji
Keyword(s):  
Electromechanical Coupling ◽  
Mechanical Performance ◽  
Vibration Energy ◽  
Electromechanical Coupling Coefficient ◽  
Mass Ratio ◽  
Modal Approach ◽  
Energy Harvesters ◽  
Cantilevered Beam ◽  
Full Analysis ◽  
Cantilevered Beams

In order to improve the performance of cantilevered vibration energy harvesters, current methods normally vary their geometric dimensions and derive the maximum power outputs by running a full analysis. This paper attempts to optimize the structural performance of cantilevered vibration energy harvesters using a modal approach without carrying out full analysis. The effects of varying geometrical dimensions on the modal mechanical performance are analysed, which includes the analysis on rectangular cantilevered beams with and without extra mass, the convergent and divergent tapered cantilevered beams. The modal approach uses mass ratio and the modal electromechanical coupling coefficient to determine the electrical and mechanical modal performance of vibration energy harvesters. In particular, mass ratio depends on the modal participation factor, and it represents the influence of modal mechanical behaviour on the power density directly. The required modal parameters are derived using the finite element method and a distributed parameter electromechanical model is also used for comparison. The cantilevered beam designs using the modal approach can be used with different sizes with the power ranging from microwatts to milliwatts.

Tapered Two-Layer Broadband Vibration Energy Harvesters

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Xingyu Xiong ◽  
S. Olutunde Oyadiji
Keyword(s):  
Power Density ◽  
Power Output ◽  
Electromechanical Coupling ◽  
Design Strategy ◽  
Dominant Mode ◽  
Vibration Energy ◽  
Electromechanical Coupling Coefficient ◽  
Mass Ratio ◽  
Energy Harvesters ◽  
Resonance Frequencies

Two-layer piezoelectric vibration energy harvesters using convergent and divergent tapered structures have been developed for broadband power output. The harvesters consist of a base cantilevered beam, which is attached to an upper beam by a spacer to develop a two-layer configuration. Two masses are attached to each layer to tune the resonance frequencies of each harvester and one of these masses also serves as the spacer. By varying the positions of the masses, the convergent and divergent tapered harvesters can generate close resonance frequencies and considerable power output in the first two modes. A broadband harvester design strategy is introduced based on a modal approach, which determines the modal performance using mass ratio and modal electromechanical coupling coefficient (EMCC). The required modal parameters are derived using the finite element method. Mass ratio represents the influence of the modal mechanical behavior on the power density directly. Since the dominant mode causes the remaining modes to have smaller mass ratios, smaller EMCC, and poor performance, the design strategy involves the selection of the harvester configurations with close resonances and favorable values of mass ratio initially, and deriving the EMCC and power density of those selected configurations.

scholarly journals Combined piezoelectric and flexoelectric effects in resonant dynamics of nanocantilevers

2018 ◽  
Vol 29 (20) ◽  
pp. 3949-3959 ◽  
Author(s):  
Adriane G Moura ◽  
Alper Erturk
Keyword(s):  
Barium Titanate ◽  
Frequency Response ◽  
Coupling Coefficient ◽  
Electromechanical Coupling ◽  
Analytical Framework ◽  
Electromechanical Coupling Coefficient ◽  
Sensors And Actuators ◽  
Energy Harvesters ◽  
Size Dependent ◽  
Resonant Dynamics

We establish and analyze an analytical framework by accounting for both the piezoelectric and flexoelectric effects in bimorph cantilevers. The focus is placed on the development of governing electroelastodynamic piezoelectric–flexoelectric equations for the problems of resonant energy harvesting, sensing, and actuation. The coupled governing equations are analyzed to obtain closed-form frequency response expressions via modal analysis. The combined piezoelectric–flexoelectric coupling coefficient expression is identified and its size dependence is explored. Specifically, a typical atomistic value of the flexoelectric constant for barium titanate is employed in the model simulations along with its piezoelectric constant from the existing literature. It is shown that the effective electromechanical coupling of a piezoelectric material, such as barium titanate, is significantly enhanced for thickness levels below 100 nm. The electromechanical coupling coefficient of a barium titanate bimorph cantilever increases from the bulk piezoelectric value of 0.065 to the combined piezoelectric–flexoelectric value exceeding 0.3 toward nanometer thickness level. Electromechanical frequency response functions for resonant power generation and dynamic actuation also capture the size-dependent enhancement of the electromechanical coupling. The analytical framework given here can be used for parameter identification and design of nanoscale cantilevers that can be used as energy harvesters, sensors, and actuators.

Assumed-Modes Formulation of Piezoelectric Energy Harvesters: Euler-Bernoulli, Rayleigh and Timoshenko Models With Axial Deformations

2010 ◽  
Author(s):  
Alper Erturk ◽  
Daniel J. Inman
Keyword(s):  
Analytical Solution ◽  
Piezoelectric Materials ◽  
Axial Direction ◽  
Vibration Energy ◽  
Power Requirement ◽  
Large Power ◽  
Energy Harvesters ◽  
Piezoelectric Energy ◽  
Cantilevered Beam ◽  
Transduction Mechanisms

Harvesting of vibration energy has been investigated by numerous researchers over the last decade. The research motivation in this field is due to the reduced power requirement of small electronic components such as wireless sensor networks used in monitoring applications. The ultimate goal is to power such devices by using the waste vibration energy available in their environment so that the maintenance requirement for battery replacement is minimized. Among the basic transduction mechanisms that can be used for vibration-to-electricity conversion, piezoelectric transduction has received the most attention due to the large power densities and ease of application of piezoelectric materials. Typically, a piezoelectric energy harvester is a cantilevered beam with one or two piezoceramic layers and the source of excitation is the base motion in the transverse direction. This paper presents general formulations for electromechanical modeling of base-excited piezoelectric energy harvesters with symmetric and asymmetric laminates. The electromechanical derivations are given using the assumed-modes method under the Euler-Bernoulli, Rayleigh and Timoshenko beam assumptions in three sections. The formulations account for an independent axial displacement variable in all cases. Comparisons are provided against the analytical solution given by the authors for symmetric laminates and convergence of the assumed-modes solution to the analytical solution with the increasing number of modes is shown. Experimental validations are also presented by comparing the electromechanical frequency response functions derived here against the experimentally obtained ones. The electromechanical assumed-modes formulations given here can be used for modeling of piezoelectric energy harvesters with asymmetric laminates as well as those with moderate thickness and varying geometry in the axial direction.

A Distributed Parameter Electromechanical Model for Cantilevered Piezoelectric Energy Harvesters

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
A. Erturk ◽  
D. J. Inman
Keyword(s):  
Electromechanical Coupling ◽  
Mechanical Response ◽  
Exact Analytical Solution ◽  
Short Circuit ◽  
Open Circuit ◽  
Distributed Parameter ◽  
Energy Harvesters ◽  
Piezoelectric Energy ◽  
Cantilevered Beams ◽  
Power Outputs

Cantilevered beams with piezoceramic layers have been frequently used as piezoelectric vibration energy harvesters in the past five years. The literature includes several single degree-of-freedom models, a few approximate distributed parameter models and even some incorrect approaches for predicting the electromechanical behavior of these harvesters. In this paper, we present the exact analytical solution of a cantilevered piezoelectric energy harvester with Euler–Bernoulli beam assumptions. The excitation of the harvester is assumed to be due to its base motion in the form of translation in the transverse direction with small rotation, and it is not restricted to be harmonic in time. The resulting expressions for the coupled mechanical response and the electrical outputs are then reduced for the particular case of harmonic behavior in time and closed-form exact expressions are obtained. Simple expressions for the coupled mechanical response, voltage, current, and power outputs are also presented for excitations around the modal frequencies. Finally, the model proposed is used in a parametric case study for a unimorph harvester, and important characteristics of the coupled distributed parameter system, such as short circuit and open circuit behaviors, are investigated in detail. Modal electromechanical coupling and dependence of the electrical outputs on the locations of the electrodes are also discussed with examples.

scholarly journals An Arc-shaped Piezoelectric Bistable Vibration Energy Harvester: Modeling and Experiments

Sensors ◽  
2018 ◽  
Vol 18 (12) ◽  
pp. 4472 ◽  
Author(s):  
Xuhui Zhang ◽  
Wenjuan Yang ◽  
Meng Zuo ◽  
Houzhi Tan ◽  
Hongwei Fan ◽  
...  
Keyword(s):  
Energy Harvesting ◽  
Electromechanical Coupling ◽  
Energy Harvester ◽  
Magnetic Coupling ◽  
Load Resistance ◽  
Vibration Energy ◽  
Electromechanical Coupling Coefficient ◽  
Vibration Energy Harvesting ◽  
Vibration Energy Harvester ◽  
Modeling And Experiments

In order to improve vibration energy harvesting, this paper designs an arc-shaped piezoelectric bistable vibration energy harvester (ABEH). The bistable configuration is achieved by using magnetic coupling, and the nonlinear magnetic force is calculated. Based on Lagrangian equation, piezoelectric theory, Kirchhoff’s law, etc., a complete theoretical model of the presented ABEH is built. The influence of the nonlinear stiffness terms, the electromechanical coupling coefficient, the damping, the distance between magnets, and the load resistance on the dynamic response and the energy harvesting performance of the ABEH is numerically explored. More importantly, experiments are designed to verify the energy harvesting enhancement of the ABEH. Compared with the non-magnet energy harvester, the ABEH has much better energy harvesting performance.

A Multi-Point Loaded Piezocomposite Beam: Modeling of Vibration Energy Harvesting

2018 ◽  
Author(s):  
Hesam Sharghi ◽  
Onur Bilgen
Keyword(s):  
Energy Harvesting ◽  
Piezoelectric Materials ◽  
Beam Theory ◽  
Vibration Energy ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Mechanical Deformations ◽  
Cantilevered Beam ◽  
Tip Velocity ◽  
Euler Bernoulli Beam

Energy harvesting from ambient vibrations and mechanical deformations using piezoelectric materials has received significant attention over the last decade. These types of energy harvesters find applications in structural health monitoring, wireless sensor networks, etc. In this paper, vibration energy harvesting from piezocomposite beams with unconventional boundary conditions is investigated. The so-called inertial four-point boundary condition is useful in applications where the cantilevered beam setup leads to non-uniform stress-strain distribution along the beam domain. In this paper, the Euler-Bernoulli beam theory is used to model the beam. The voltage output, maximum power output, and the tip velocity are investigated. The efficiency of the four-point loaded beam is compared to a cantilever beam.

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