Stiffness control of a nonlinear mechanical folded beam for wideband vibration energy harvesters

2018 ◽  
Vol 85 (9) ◽  
pp. 553-564 ◽  
Author(s):  
Mohamed Amri ◽  
Philippe Basset ◽  
Dimitri Galayko ◽  
Francesco Cottone ◽  
Einar Halvorsen ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
Order Approximation ◽  
Perturbation Technique ◽  
Time Integration ◽  
Vibration Energy ◽  
Vibration Energy Harvesting ◽  
Folding Angle ◽  
Energy Harvesters ◽  
Nonlinear Springs ◽  
Novel Approach

Abstract This paper presents a novel approach to design and optimize geometric nonlinear springs for wideband vibration energy harvesting. To this end, we designed a spring with several folds to increase its geometric nonlinearities. A numerical analysis is performed using the Finite Element Method to estimate its quadratic and cubic spring stiffness. A nonlinear effective spring constant is then calculated for different values of the main folding angle. We demonstrate that this angle can increase nonlinearities within the structure resulting in higher bandwidths, and that it is possible to control the behavior of the system to have softening-type or hardening-type response depending on the choice of the folding angle. Based on the Lindstedt-Poincaré perturbation technique, a first order approximation is determined to predict the frequency-response of the system. In order to validate the perturbation analysis, numerical solutions based on long-time integration method and mixed VHDL-AMS/Spice simulations are presented. Finally, this method is applied to a previously published device and shows a good agreement with experiments.

scholarly journals Nonlinear H-Shaped Springs to Improve Efficiency of Vibration Energy Harvesters

2013 ◽  
Vol 80 (6) ◽  
Author(s):  
Sebastien Boisseau ◽  
Ghislain Despesse ◽  
Bouhadjar Ahmed Seddik
Keyword(s):  
Output Power ◽  
Mechanical Energy ◽  
Resonance Phenomenon ◽  
Vibration Energy ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Nonlinear Springs ◽  
Working Frequency ◽  
Nonlinear Devices ◽  
Mass Spring

Vibration energy harvesting is an emerging technology aimed at turning mechanical energy from vibrations into electricity to power the microsystems of the future. Most current vibration energy harvesters (VEH) are based on a mass-spring structure: this introduces a resonance phenomenon that enables an increase of VEH output power (compared to nonresonant systems); however, the working frequency bandwidth is limited. Therefore, these devices are not able to harvest energy when ambient vibrations’ frequencies shift. To solve this problem and to increase the frequency band where power can be harvested, one solution consists in using nonlinear springs. This paper introduces H-shaped nonlinear springs, their model, and their benefits to improve VEH output powers. Simulations on real vibration sources show that the output power can be higher in nonlinear devices (up to +48%) compared to linear systems.

scholarly journals Enhanced low-frequency vibration energy harvesting with inertial amplifiers

2021 ◽  
pp. 1045389X2110322
Author(s):  
Sondipon Adhikari ◽  
Arnab Banerjee
Keyword(s):  
Low Frequency ◽  
Vibration Energy ◽  
Vibration Energy Harvesting ◽  
Micro Scale ◽  
Energy Harvesters ◽  
Low Frequency Vibration ◽  
Different Types ◽  
Mechanical Approach ◽  
Ambient Excitation ◽  
Piezoelectric Vibration

Piezoelectric vibration energy harvesters have demonstrated the potential for sustainable energy generation from diverse ambient sources in the context of low-powered micro-scale systems. However, challenges remain concerning harvesting more power from low-frequency input excitations and broadband random excitations. To address this, here we propose a purely mechanical approach by employing inertial amplifiers with cantilever piezoelectric vibration energy harvesters. The proposed mechanism can achieve inertial amplification amounting to orders of magnitude under certain conditions. Harmonic, as well as broadband random excitations, are considered. Two types of harvesting circuits, namely, without and with an inductor, have been employed. We explicitly demonstrate how different parameters describing the inertial amplifiers should be optimally tuned to maximise harvested power under different types of excitations and circuit configurations. It is possible to harvest five times more power at a 50% lower frequency when the ambient excitation is harmonic. Under random broadband ambient excitations, it is possible to harvest 10 times more power with optimally selected parameters.

Transfer Function Modeling of Distributed Piezoelectric Vibration Energy Harvesters

2009 ◽  
Author(s):  
Chin An Tan ◽  
Heather L. Lai
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Vibration Energy ◽  
System Response ◽  
Distributed Parameter ◽  
Domain Modeling ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Adjoint Systems ◽  
The Stability

Extensive research has been conducted on vibration energy harvesting utilizing a distributed piezoelectric beam structure. A fundamental issue in the design of these harvesters is the understanding of the response of the beam to arbitrary external excitations (boundary excitations in most models). The modal analysis method has been the primary tool for evaluating the system response. However, a change in the model boundary conditions requires a reevaluation of the eigenfunctions in the series and information of higher-order dynamics may be lost in the truncation. In this paper, a frequency domain modeling approach based in the system transfer functions is proposed. The transfer function of a distributed parameter system contains all of the information required to predict the system spectrum, the system response under any initial and external disturbances, and the stability of the system response. The methodology proposed in this paper is valid for both self-adjoint and non-self-adjoint systems, and is useful for numerical computer coding and energy harvester design investigations. Examples will be discussed to demonstrate the effectiveness of this approach for designs of vibration energy harvesters.

Multi-Modal Vibration Energy Harvesting Using a Trapezoidal Plate

2011 ◽  
Author(s):  
Mustafa H. Arafa
Keyword(s):  
System Performance ◽  
Energy Harvester ◽  
Natural Frequencies ◽  
Vibration Energy ◽  
Vibration Modes ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Trapezoidal Plate ◽  
Plate Geometry ◽  
Modal Vibration

Vibration-based energy harvesters are usually designed to exhibit natural frequencies that match those of the excitation for maximum power output. This has spurred interest into the design of devices that respond to variable frequency sources. In this work, an electromagnetic energy harvester in the form of a base excited trapezoidal plate is proposed. The plate geometry is designed to achieve two closely spaced vibration modes in order to harvest energy across a broader bandwidth. The ensuing bending and twisting vibrations are utilized in this capacity by placing a magnet on the plate tip that moves past a stationary coil. A dynamic model is presented to predict the system performance and is verified experimentally.

Investigation of Vibration Energy Harvesting Using Two Cantilevers With Random Input

2017 ◽  
Author(s):  
Wei Yang ◽  
Panagiotis Alevras ◽  
Shahrzad Towfighian
Keyword(s):  
Mechanical Energy ◽  
Duffing Oscillator ◽  
Electrical Energy ◽  
Potential Energy Function ◽  
Excitation Level ◽  
Vibration Energy ◽  
Random Input ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Low Performance

There is a growing interest to convert ambient mechanical energy to electrical energy by vibration energy harvesters. Realistic vibrations are random and spread over a large frequency range. Most energy harvesters are linear with narrow frequency bandwidth and show low performance, which led to creation of nonlinear harvesters that have larger bandwidth. This article presents a simulation study of a nonlinear energy harvester that contains two cantilever beams coupled by magnetic force. One of the cantilever beam is covered partially by piezoelectric material, while the other beam is normal to the first one and is used to create a variable potential energy function. The variable double-well potential function enables optimum conversion of the kinetic energy and thus larger output. The system is modeled by coupled Duffing oscillator equations. To represent the ambient vibrations, the response to Gaussian random input signal (generated by Shinozuka formula) is studied using power spectral density. The effects of different parameters on the system are also investigated. The results show that the double cantilever harvester has a threshold distance, where the harvester can perform optimally regardless of the excitation level. This observation is opposite to that of the conventional fixed magnet cantilever system where the optimal distance varies with the excitation level. Results of this study can be used to enhance energy efficiency of vibration energy harvesters.

scholarly journals Improving functionality of vibration energy harvesters using magnets

2012 ◽  
Vol 23 (13) ◽  
pp. 1433-1449 ◽  
Author(s):  
Lihua Tang ◽  
Yaowen Yang ◽  
Chee-Kiong Soh
Keyword(s):  
Experimental Study ◽  
Energy Harvesting ◽  
Transition Region ◽  
Parametric Study ◽  
Low Frequency ◽  
Design Guidelines ◽  
Vibration Energy ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Low Frequency Vibration

In recent years, several strategies have been proposed to improve the functionality of energy harvesters under broadband vibrations, but they only improve the efficiency of energy harvesting under limited conditions. In this work, a comprehensive experimental study is conducted to investigate the use of magnets for improving the functionality of energy harvesters under various vibration scenarios. First, the nonlinearities introduced by magnets are exploited to improve the performance of vibration energy harvesting. Both monostable and bistable configurations are investigated under sinusoidal and random vibrations with various excitation levels. The optimal nonlinear configuration (in terms of distance between magnets) is determined to be near the monostable-to-bistable transition region. Results show that both monostable and bistable nonlinear configurations can significantly outperform the linear harvester near this transition region. Second, for ultra-low-frequency vibration scenarios such as wave heave motions, a frequency up-conversion mechanism using magnets is proposed. By parametric study, the repulsive configuration of magnets is found preferable in the frequency up-conversion technique, which is efficient and insensitive to various wave conditions when the magnets are placed sufficiently close. These findings could serve as useful design guidelines when nonlinearity or frequency up-conversion techniques are employed to improve the functionality of vibration energy harvesters.

Multi-Modal Vibration Energy Harvesting Using a Trapezoidal Plate

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Mustafa H. Arafa
Keyword(s):  
System Performance ◽  
Energy Harvester ◽  
Natural Frequencies ◽  
Vibration Energy ◽  
Vibration Modes ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Trapezoidal Plate ◽  
Plate Geometry ◽  
Modal Vibration

Vibration-based energy harvesters are usually designed to exhibit natural frequencies that match those of the excitation for maximum power output. This has spurred interest into the design of devices that respond to variable frequency sources. In this work, an electromagnetic energy harvester in the form of a base excited trapezoidal plate is proposed. The plate geometry is designed to achieve two closely spaced vibration modes in order to harvest energy across a broader bandwidth. The ensuing bending and twisting vibrations are utilized in this capacity by placing a magnet on the plate tip that moves past a stationary coil. A dynamic model is presented to predict the system performance and is verified experimentally.

Enhanced Energy Harvesting of a Nonlinear Energy Sink by Internal Resonance

2019 ◽  
Vol 11 (10) ◽  
pp. 1950100 ◽  
Author(s):  
Shuai Hou ◽  
Ying-Yuan Teng ◽  
Ye-Wei Zhang ◽  
Jian Zang
Keyword(s):  
Energy Harvesting ◽  
Internal Resonance ◽  
Numerical Solutions ◽  
Nonlinear Energy Sink ◽  
Vibration Energy ◽  
Resonance System ◽  
Vibration Energy Harvesting ◽  
Energy Sink ◽  
The Relationship ◽  
Nonlinear Energy

Given its essential nonlinearity, nonlinear energy sink (NES) has been extensively studied as a promising vibration energy harvesting device. Internal resonance, which is due to strong energy exchange between modes, also provides a valuable idea for vibration energy harvesting. Combining these two advantages, we put forward a 3:1 internal resonance system, which consists of an NES and a coupled linear oscillator, as an enhanced method for vibration energy harvesting. The multiscale method is applied to derive the relationship between amplitude and frequency response. Simulations are carried out to evaluate the performance of the proposed method. Results show that the internal resonance system can remarkably improve the vibration energy harvesting performance. The numerical solutions verify the accuracy of the analytical solutions. The results demonstrate that the internal resonance system with NES for energy harvesting has better output power and bandwidth compared with noninternal resonance system. Overall, the comprehensive design improves the performance of NES for vibration energy harvesting.

Experimental characterisation of dual-mass vibration energy harvesters employing velocity amplification

2016 ◽  
Vol 27 (20) ◽  
pp. 2810-2826 ◽  
Author(s):  
Ronan Frizzell ◽  
Gerard Kelly ◽  
Francesco Cottone ◽  
Elisabetta Boco ◽  
Valeria Nico ◽  
...  
Keyword(s):  
Frequency Response ◽  
Energy Harvester ◽  
Wireless Sensor ◽  
Vibration Energy ◽  
Vibration Energy Harvesting ◽  
Vibration Energy Harvester ◽  
Energy Harvesters ◽  
Network Applications ◽  
Higher Power ◽  
Battery Technology

Vibration energy harvesting extracts energy from the environment and can mitigate reliance on battery technology in wireless sensor networks. This article presents the nonlinear responses of two multi-mass vibration energy harvesters that employ a velocity amplification effect. This amplification is achieved by momentum transfer from larger to smaller masses following impact between masses. Two systems are presented that show the evolution of multi-mass vibration energy harvester designs: (1) a simplified prototype that effectively demonstrates the basic principles of the approach and (2) an enhanced design that achieves higher power densities and a wider frequency response. Various configurations are investigated to better understand the nonlinear dynamics and how best to realise future velocity-amplified vibration energy harvesters. The frequency responses of the multi-mass harvesters show that these devices have the potential to reduce risks associated with deploying vibration energy harvester devices in wireless sensor network applications; the wide frequency response reduces the need to re-tune the harvesters following frequency variations of the source vibrations.

Electrostatic Vibration Energy Harvesters with Linear and Nonlinear Resonators

2014 ◽  
Vol 24 (11) ◽  
pp. 1430030 ◽  
Author(s):  
Peter Harte ◽  
Elena Blokhina ◽  
Orla Feely ◽  
Danièle Fournier-Prunaret ◽  
Dimitri Galayko
Keyword(s):  
Steady State ◽  
Multiple Scales ◽  
Perturbation Technique ◽  
Period Doubling ◽  
Vibration Energy ◽  
Energy Harvesters ◽  
Transition To Chaos ◽  
Nonlinear Resonator ◽  
Linear And Nonlinear ◽  
Filippov Type

This paper discusses the time-dependent dynamics of electrostatic vibration energy harvesters (eVEHs) with linear and nonlinear mechanical resonators. These eVEHs are fundamentally nonlinear regardless of whether a linear or nonlinear resonator is being used. The model of the system under investigation has the form of a piecewise-smooth dynamical system of a Filippov type that has a specific discontinuity in the form of a hold-on term. We use a perturbation technique called the multiple scales method to develop a theory to analyze the steady-state dynamics of the system, be it with a linear or a nonlinear resonator. We then analyze the stability of the steady-state orbit to determine when the first doubling bifurcation occurs in the system. This gives an upper bound on the region of steady-state oscillations which allows us to determine a theoretical limit on the power convertible by the eVEH. We then turn our discussion to the nonlinear behavior we see in the system's transition to chaos. Since the eVEH studied here is a Filippov type system, sliding modes and sliding bifurcations are possible in the system. We discuss the evolution of the sliding region and give particular examples of sliding phenomena and sliding bifurcations. An understanding of sliding phenomena is required for analyzing the transition to chaos since segments of sliding motion appear on trajectories that undergo period-doubling bifurcations. The transition to chaos is explained in detail by the example of the system with a linear resonator, however we discuss examples of the system with mechanical nonlinearities and discuss the difference between the linear and nonlinear cases.

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