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.

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.

Multimodal Energy Harvesting System: Piezoelectric and Electromagnetic

2008 ◽  
Vol 20 (5) ◽  
pp. 625-632 ◽  
Author(s):  
Yonas Tadesse ◽  
Shujun Zhang ◽  
Shashank Priya
Keyword(s):  
Energy Harvesting ◽  
Resonance Frequency ◽  
Permanent Magnet ◽  
Cantilever Beam ◽  
Piezoelectric Energy Harvesting ◽  
Prototype System ◽  
Finite Element Software ◽  
Piezoelectric Energy ◽  
Energy Harvesting System ◽  
Tip Mass

In this study, we report a multimodal energy harvesting device that combines electromagnetic and piezoelectric energy harvesting mechanism. The device consists of piezoelectric crystals bonded to a cantilever beam. The tip of the cantilever beam has an attached permanent magnet which, oscillates within a stationary coil fixed to the top of the package. The permanent magnet serves two purpose (i) acts as a tip mass for the cantilever beam and lowers the resonance frequency, and (ii) acts as a core which oscillates between the inductive coils resulting in electric current generation through Faraday's effect. Thus, this design combines the energy harvesting from two different mechanisms, piezoelectric and electromagnetic, on the same platform. The prototype system was optimized using the finite element software, ANSYS, to find the resonance frequency and stress distribution. The power generated from the fabricated prototype was found to be 0.25 W using the electromagnetic mechanism and 0.25 mW using the piezoelectric mechanism at 35 g acceleration and 20 Hz frequency.

Nonlinear Vibration of a Magneto-Elastic Cantilever Beam With Tip Mass

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Barun Pratiher ◽  
Santosha K. Dwivedy
Keyword(s):  
Magnetic Field ◽  
Frequency Response ◽  
Cantilever Beam ◽  
Multiple Scales ◽  
Flexible Structures ◽  
Nonlinear Damping ◽  
Equation Of Motion ◽  
Response Curves ◽  
Temporal Form ◽  
Tip Mass

In this work the effect of the application of an alternating magnetic field on the large transverse vibration of a cantilever beam with tip mass is investigated. The governing equation of motion is derived using D’Alembert’s principle, which is reduced to its nondimensional temporal form by using the generalized Galerkin method. The temporal equation of motion of the system contains nonlinearities of geometric and inertial types along with parametric excitation and nonlinear damping terms. Method of multiple scales is used to determine the instability region and frequency response curves of the system. The influences of the damping, tip mass, amplitude of magnetic field strength, permeability, and conductivity of the beam material on the frequency response curves are investigated. These perturbation results are found to be in good agreement with those obtained by numerically solving the temporal equation of motion and experimental results. This work will find extensive applications for controlling vibration in flexible structures using a magnetic field.

Powering Pacemakers With a Nonlinear Hybrid Rotary-Translational Energy Harvester

2014 ◽  
Author(s):  
Benjamin Kuch ◽  
M. Amin Karami
Keyword(s):  
Energy Harvesting ◽  
Multiple Scales ◽  
Mechanical Energy ◽  
Sine Wave ◽  
Translational Energy ◽  
Medical Problems ◽  
Energy Harvesting System ◽  
Energy Harvesting Devices ◽  
Insight Into ◽  
Nonlinear Hybrid

An application of a nonlinear Hybrid Rotary-Translational (HRT) generator is presented. An HRT generator differs from traditional energy harvesting devices in that it has the ability to harvest multi-axis base excitation. The device consists of a pendulum-like system whose rotations are caused by the base excitations. The swinging pendulum is coupled to a direct current micro generator to generate electricity. The considered application is the energy harvesting from heartbeat induced vibrations. The motivation behind studying the effectiveness of this application comes from battery hindrance. The use of relatively large batteries to power pacemakers presents many medical problems, including increasing the size of the device to accommodate the battery causing surgery complications as well as needing periodic battery replacement. An energy harvesting device can eliminate the need for such a battery, relying instead on the power generated by the beating heart. The nonlinearity of the device allows constant power to be generated across a wider range of frequencies (heartbeats per minute). The contractions of the heart are considered to be the base excitations of the device, causing the pendulum to swing. To validate and then optimize the design of the HRT system, the behavior and the power generation of the system will be studied under different parameters: size of generator, mass and length of pendulum components as well as frequency of heart beats (beats per minute). This presents an interesting design problem whose goal is to find the best HRT parameters that would result in generating the sufficient amounts of power required by pacemakers. A method in approximating the nonlinear dynamics of the electro-mechanical energy harvesting system is also presented. By studying the analytical solutions to the nonlinear electromechanical system under a sine wave excitation, we can gain insight into the problem. The extent of this paper will only cover the analytical solution to the vertically excited pendulum. Perturbation methods, specifically the multiple scales method will be employed to study the effects of forcing amplitude and frequency on the system behavior and the energy harvesting system.

scholarly journals A Low-Frequency MEMS Piezoelectric Energy Harvesting System Based on Frequency Up-Conversion Mechanism

Micromachines ◽  
2019 ◽  
Vol 10 (10) ◽  
pp. 639 ◽  
Author(s):  
Manjuan Huang ◽  
Cheng Hou ◽  
Yunfei Li ◽  
Huicong Liu ◽  
Fengxia Wang ◽  
...  
Keyword(s):  
Energy Harvesting ◽  
High Frequency ◽  
Low Frequency ◽  
Piezoelectric Energy Harvesting ◽  
Piezoelectric Energy ◽  
Mems Fabrication ◽  
Piezoelectric Cantilever ◽  
Energy Harvesting System ◽  
Micro Electromechanical System ◽  
The Impact

This paper proposes an impact-based micro piezoelectric energy harvesting system (PEHS) working with the frequency up-conversion mechanism. The PEHS consists of a high-frequency straight piezoelectric cantilever (SPC), a low-frequency S-shaped stainless-steel cantilever (SSC), and supporting frames. During the vibration, the frequency up-conversion behavior is realized through the impact between the bottom low-frequency cantilever and the top high-frequency cantilever. The SPC used in the system is fabricated using a new micro electromechanical system (MEMS) fabrication process for a piezoelectric thick film on silicon substrate. The output performances of the single SPC and the PEHS under different excitation accelerations are tested. In the experiment, the normalized power density of the PEHS is 0.216 μW·g−1·Hz−1·cm−3 at 0.3 g acceleration, which is 34 times higher than that of the SPC at the same acceleration level of 0.3 g. The PEHS can improve the output power under the low frequency and low acceleration scenario.

scholarly journals Duffing Oscillator With Parametric Excitation: Analytical and Experimental Investigation on a Belt-Pulley System

2008 ◽  
Vol 3 (3) ◽  
Author(s):  
Guilhem Michon ◽  
Lionel Manin ◽  
Robert G. Parker ◽  
Régis Dufour
Keyword(s):  
Experimental Investigation ◽  
Nonlinear Response ◽  
Multiple Scales ◽  
Duffing Oscillator ◽  
Equation Of Motion ◽  
Viscous Damping ◽  
Pulley System ◽  
Transverse Vibrations ◽  
Proposed Model ◽  
Complex Phenomena

This paper is devoted to the theoretical and experimental investigation of a sample automotive belt-pulley system subjected to tension fluctuations. The equation of motion for transverse vibrations leads to a Duffing oscillator parametrically excited. The analysis is performed via the multiple scales approach for predicting the nonlinear response, considering longitudinal viscous damping. An experimental setup gives rise to nonlinear parametric instabilities and also exhibits more complex phenomena. The experimental investigation validates the assumptions made and the proposed model.

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