Analytical Approximation and Experimental Study of Bi-Stable Hybrid Nonlinear Energy Harvesting System

2011 ◽  
Author(s):  
M. Amin Karami ◽  
Paulo S. Varoto ◽  
Daniel J. Inman
Keyword(s):  
Experimental Study ◽  
Energy Harvesting ◽  
Limit Cycles ◽  
Electromechanical Coupling ◽  
Multiple Scales ◽  
Duffing Oscillator ◽  
Excitation Frequency ◽  
Stable Configuration ◽  
Hybrid Energy ◽  
Energy Harvesting System

The paper presents modeling, analytical investigation and experimental study of a nonlinear hybrid energy harvesting system in the bi-stable configuration. Linear energy harvesters are frequency sensitive meaning they only generate reasonable power if they are excited accurately at their first natural frequency. Nonlinear effects can be used to increase the effective range of excitations frequency by broadening the frequency response. The proposed hybrid energy harvester uses Piezoelectric and Electromagnetic transduction mechanisms. Electromechanical coupling has been included in the study of the nonlinear dynamics of the harvester. The shooting method has been used to numerically calculate the limit cycles of the bi-stable system. The calculated limit cycles and the Poincare map of the system give the big picture of system vibrations due to the base accelerations. An approximation method is suggested using the method of multiple scales and verified by numerical integrations to find an equivalent forced, damped Duffing oscillator for the original harvesting system. The approximation results the equivalent mechanical system that acts similar to the coupled electromechanical harvester. The approximation is a function of the harvesting circuit so the back coupling is not overlooked. Meanwhile the amount of computations and the complexity of the problem are significantly reduced. The nonlinear vibration of the proposed nonlinear bi-stable harvester is also experimentally investigated. The study shows that the Limit Cycle Oscillations of the nonlinear system increase the power production by two orders of magnitude. The relations between the power output and the excitation level, the excitation frequency, and the electric loads are investigated.

Modeling of a Vibration-Based Piezomagnetoelastic Energy Harvesting System by Using the Duffing Equation

2012 ◽  
Author(s):  
Henrik Westermann ◽  
Marcus Neubauer ◽  
Jörg Wallaschek
Keyword(s):  
Energy Harvesting ◽  
Multiple Scales ◽  
Duffing Oscillator ◽  
Harmonic Balance Method ◽  
Equation Of Motion ◽  
Duffing Equation ◽  
Restoring Force ◽  
Piezoelectric Cantilever ◽  
Energy Harvesting System ◽  
Tip Mass

This article illustrates the modeling of a piezomagnetoelastic energy harvesting system. The generator consists of a piezoelectric cantilever with a magnetic tip mass. A second oppositely poled magnet is attached near the free end of the beam. Due to the nonlinear magnetic restoring force the system exhibits two symmetric stable equilibrium positions and one instable equilibrium position. The equation of motion is derived and it is shown that the system can be modeled as Duffing oscillator. An analytical approach is given to derive the Duffing parameters from the system parameters. The Duffing equation is solved for an oscillation around both equilibrium positions by using the harmonic balance method. For small orbit oscillations the equation of motion is solved by applying the fourth-order multiple scales method.

Modeling of a Nonlinear Vibration-Based Energy Harvesting System as a Duffing Oscillator

2013 ◽  
Vol 198 ◽  
pp. 663-668
Author(s):  
Henrik Westermann ◽  
Marcus Neubauer ◽  
Jörg Wallaschek
Keyword(s):  
Energy Harvesting ◽  
Resonant Frequency ◽  
Nonlinear Oscillator ◽  
Duffing Oscillator ◽  
Excitation Frequency ◽  
Cantilever Structure ◽  
Energy Harvesting System ◽  
Harvesting Techniques ◽  
Host Structure ◽  
Tip Mass

The harvesting of ambient energy has become more important over the last years. This paper will investigate an analytical effort to predict the Duffing parameters for a magnetoelastic cantilever structure. The modeling is compared to a nonlinear harvester with point dipoles. The system consists of a harmonic excited cantilever structure with a magnetic tip mass. The beam is firmly clamped to the host structure. A second oppositely poled permanent magnet is located near the free end of the beam. The system is a bistable nonlinear oscillator with two equilibrium positions. Several studies show the better performance of the setup. The approach is not limited for energy harvesting techniques. The setup is suitable for broadband oscillations and also to tune the resonant frequency closer to the excitation frequency.

The Application of Electrode Design in Vibrating Piezoceramic Plate for Energy Harvesting System

2013 ◽  
Author(s):  
Yu-Hsi Huang ◽  
Ching-Kong Chao ◽  
Wan-Ting Chou
Keyword(s):  
Energy Harvesting ◽  
Dynamic Characteristics ◽  
Electromechanical Coupling ◽  
Coupling Efficiency ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Experimental Measurements ◽  
Piezoceramic Plate ◽  
Resonant Frequencies ◽  
Energy Harvesting System

The energy harvesting system of piezoceramic plate is studied on the electrode configuration to improve the electromechanical transferring efficiency. The piezoceramic plate is used to perform the vibration characteristics by experimental measurements and finite element method (FEM). Thereafter, the dynamic characteristics and the electromechanical coupling efficiency of the piezoelectric energy harvesting system are studied by the electrode design method of the piezoceramic plate. Several experimental techniques are used to measure the dynamic characteristics of piezoceramic plate. First, the full-filed optical technique, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), can measure simultaneously the resonant frequencies and mode shapes for out-of-plane and in-plane vibrations. Second, the pointwisely measuring system, laser Doppler vibrometer (LDV), can obtain resonant frequencies by dynamic signal swept-sine analysis. Third, the correspondent in-plane resonant frequencies and anti-resonant frequencies are obtained by impedance analysis. The experimental results of vibration characteristics are verified with numerical calculations. Besides the dynamic characteristics of piezoceramic plates are analyzed in converse piezoelectric effect, the direct piezoelectric effect of piezoceramic plates are excited by shaker to generate the electric voltage. It has excellent consistence between resonant frequencies and mode shapes on the vibration characteristics by experimental measurements and finite element numerical calculations. In this study, the Electrical Potential Gradient (EPG) calculated by FEM is proposed to evaluate the electromechanical coupling efficiency of piezoceramic plate on the specific vibration mode. The correspondent electrode configuration, which is designed by EPG, can produce the best electromechanical transfer both in direct and converse piezoelectric effects. It is concluded that the vibration characteristics of piezoelectric materials have excellent consistence determined by experimental measurements and FEM.

Energy Harvesting From Impulsive Loads Using Intentional Essential Nonlinearities

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
D. Dane Quinn ◽  
Angela L. Triplett ◽  
Alexander F. Vakakis ◽  
Lawrence A. Bergman
Keyword(s):  
Energy Harvesting ◽  
Electromechanical Coupling ◽  
Piezoelectric Element ◽  
Nonlinear Behavior ◽  
Harmonic Excitation ◽  
Frequency Interval ◽  
Resistive Load ◽  
Nonlinear Harvesting ◽  
Energy Harvesting System ◽  
Energy Harvesting Devices

Energy harvesting devices designed with intentional nonlinearities offer the possibility of increased performance under broadband excitations and realistic environmental conditions. This work considers an energy harvesting system based on the response of an attachment with strong nonlinear behavior. The electromechanical coupling is achieved with a piezoelectric element across a resistive load. When the system is subject to harmonic excitation, the harvested power from the nonlinear system exhibits a wider interval of frequencies over which the harvested power is significant, although an equivalent linear device offers greater efficiency at its design frequency. However, for impulsive excitation, the performance of the nonlinear harvesting system exceeds the corresponding linear system in terms of both magnitude of power harvested and the frequency interval over which significant power can be drawn from the mechanical vibrations.

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