An M-Shaped Asymmetric Nonlinear Oscillator for Broadband Energy Harvesting

2013 ◽  
Author(s):  
S. Leadenham ◽  
A. Erturk
Keyword(s):  
Energy Harvesting ◽  
Nonlinear Oscillator ◽  
Mechanical Load ◽  
Nonlinear Behavior ◽  
Base Excitation ◽  
Lumped Mass ◽  
Response Curves ◽  
Restoring Force ◽  
Bandwidth Enhancement ◽  
Shaped Beam

Nonlinear oscillators have been given growing attention due to their ability to enhance the performance of energy harvesting devices by increasing the frequency bandwidth. Duffing oscillators are a typical type of nonlinear oscillator characterized by a symmetric hardening or softening cubic restoring force. In order to realize the cubic nonlinearity in a cantilever at reasonable excitation levels, often an external magnetic field or mechanical load is imposed, since the inherent geometric nonlinearity would otherwise require impractically high excitation levels to be pronounced. As an alternative to magnetoelastic structures and other forms of symmetric Duffing oscillators, in this paper, an M-shaped bent beam with clamped end conditions is investigated for bandwidth enhancement under base excitation. The M-shaped beam geometry can exhibit significantly asymmetric spring behavior: hardening in one direction and softening in the other. A particular advantage of the M-shaped structure is its well-pronounced nonlinear characteristics without needing an external component to create hardening or softening. The force-displacement relationship of the M-shaped beam with a central lumped mass attachment is experimentally identified and asymmetric nonlinear behavior is verified. The purely elastic system parameters (such as the linear and nonlinear stiffness components) identified from the experiments are used in numerical simulations and compared with the experimental results. A quadratic damping term is included to account for nonlinear dissipative effects. Bandwidth enhancement with increasing base excitation is investigated experimentally and numerically. Very good agreement is observed between the simulated frequency response curves and experimental measurements.

Nonlinear Dissipative Electroelastic Dynamics of an M-Shaped Broadband Piezoelectric Energy Harvester

2014 ◽  
Author(s):  
Stephen Leadenham ◽  
Alper Erturk
Keyword(s):  
Energy Harvesting ◽  
Energy Harvester ◽  
Coupled System ◽  
Spring Steel ◽  
Base Excitation ◽  
Structural Configuration ◽  
Modeling Framework ◽  
Restoring Force ◽  
Bandwidth Enhancement ◽  
Piezoelectric Energy

The use of nonlinear dynamic phenomena for frequency bandwidth enhancement in vibration-based energy harvesting has received growing attention over the last few years. Various designs have been studied to create Duffing oscillators usually by introducing magnetoelastic coupling. In such devices, magnetic forces are typically coupled with elastic beams involving ferromagnetic components to achieve a nonlinear restoring force of the monostable or bistable Duffing type. Other than the increased volume and structural complexity due to additional magnets and discrete components, these magnetoelastic piezoelectric energy harvesters are not suitable to use in various compact applications and in systems that are sensitive to magnetic fields. The M-shaped structural configuration studied in this work overcomes these issues due to the asymmetric stiffness nonlinearity created by a simple structural configuration composed of a bent spring steel beam with piezoelectric patches. The electroelastic dynamics of the M-shaped broadband piezoelectric energy harvester is governed by various interacting nonlinearities, such as the deliberately introduced stiffness nonlinearity of hardening type resulting from the substrate geometry, inherent elastic nonlinearities of softening type as well as hysteretic losses associated with piezoelectric patches, and other dissipative effects due to large velocities experienced in response to base excitation. A recently developed nonlinear non-conservative electroelastic modeling framework for the piezoelectric patches is combined with geometric nonlinearities of the M-shaped energy harvester to establish a nonlinear dissipative model of the electromechanically coupled system. Energy harvesting experiments for a set of resistors and base excitation levels are then performed to experimentally characterize the bandwidth enhancement using the M-shaped broadband piezoelectric energy harvester.

Dynamic Response of Nonlinear Oscillators With Hysteresis

2015 ◽  
Author(s):  
Biagio Carboni ◽  
Walter Lacarbonara
Keyword(s):  
Hysteresis Loops ◽  
Base Excitation ◽  
Response Curves ◽  
Restoring Force ◽  
Single Degree Of Freedom ◽  
Wire Ropes ◽  
Dynamical Behaviors ◽  
Nonlinear Features ◽  
Restoring Forces ◽  
Force Displacement

The nonlinear features of the steady-state periodic response of hysteretic oscillators are investigated. Frequency-response curves of base-excited single-degree-of-freedom (SDOF) systems possessing different hysteretic restoring forces are numerically obtained employing a continuation procedure based on the Jacobian of the Poincaré map. The memory-dependent restoring forces are expressed as a direct summation of linear and cubic elastic components and a hysteretic part described by a modified version of the Bouc-Wen law. The resulting force-displacement curves feature a pinching around the origin. Depending on the hysteresis material parameters (which regulate the shapes of the hysteresis loops), the oscillator exhibits hardening, softening and softening-hardening behaviors in which the switching from softening to hardening takes place above certain base excitation amplitudes. A comprehensive analysis in the parameters space is performed to identify the thresholds of these different behaviors. The restoring force features here considered have been experimentally obtained by means of an original rheological device comprising assemblies of steel and shape memory wire ropes. This study is carried out also with the aim of designing the restoring forces which give rise to dynamical behaviors useful for a variety of applications.

Nonlinear Two-to-One Internal Resonance for Broadband Energy Harvesting

2015 ◽  
Author(s):  
D. X. Cao ◽  
S. Leadenham ◽  
A. Erturk
Keyword(s):  
Energy Harvesting ◽  
Frequency Response ◽  
Internal Resonance ◽  
Numerical Solutions ◽  
Primary Resonance ◽  
Frame Structure ◽  
Response Curves ◽  
Current Effort ◽  
Bandwidth Enhancement ◽  
Piezoelectric Coupling

The transformation of waste vibration energy into low-power electricity has been heavily researched to enable self-sustained wireless electronic components. Monostable and bistable nonlinear oscillators have been explored by several researchers in an effort to enhance the frequency bandwidth of operation. Linear two degree of freedom (2-DOF) configurations as well as combination of a nonlinear single-DOF harvester with a linear oscillator to constitute a nonlinear 2-DOF harvester have also been explored to develop broadband energy harvesters. In the present work, the concept of nonlinear internal resonance in a continuous frame structure is explored for broadband energy harvesting. The L-shaped beam-mass structure with quadratic nonlinearity was formerly studied in the nonlinear dynamics literature to demonstrate modal energy exchange and the saturation phenomenon when carefully tuned for two-to-one internal resonance. In the current effort, piezoelectric coupling is introduced, and electromechanical equations of the L-shaped energy harvester are employed to explore the primary resonance behaviors around the first and the second linear natural frequencies for bandwidth enhancement. Simulations using approximate analytical frequency response equations as well as time-domain numerical solutions reveal that 2-DOF configuration with quadratic and two-to-one internal resonance could extend the bandwidth enhancement capability. Both electrical power and shunted vibration frequency response curves of steady-state solutions are explored in detail. Effects of various electromechanical system parameters, such as piezoelectric coupling and load resistance, on the overall dynamics of the internal resonance energy harvesting system are reported.

Dual-mass electromagnetic energy harvesting from galloping oscillations and base excitation

2020 ◽  
pp. 095440622094891
Author(s):  
Danilo Karličić ◽  
Milan Cajić ◽  
Sondipon Adhikari
Keyword(s):  
Fluid Flow ◽  
Energy Harvesting ◽  
Nonlinear Oscillator ◽  
Bluff Body ◽  
Average Power ◽  
Electromagnetic Energy ◽  
Transverse Displacement ◽  
Base Excitation ◽  
Electromagnetic Energy Harvesting ◽  
Electromagnetic Generator

This paper investigates electromagnetic energy harvesting based on vibration energy extraction from the vibration of a bluff body elastically connected with an additional nonlinear oscillator and subjected to fluid flow and base excitation. The mechanical part is modeled as a system of two coupled oscillators where a combination of harmonic base excitation and fluid forces leads to a steady-state regime. The electromagnetic generator as part of the harvesting device is represented by the equivalent electrical circuit with power dissipated at an electrical load resistance. The mathematical model is based on a set of two coupled nonlinear ordinary differential equations considering the transverse displacement of a bluff body, additional nonlinear oscillator, and currents induced in the electromagnetic generator. By introducing the incremental harmonic balance and continuation methods nonlinear periodic responses are investigated and complex dynamic behavior presented through corresponding response diagrams. The results indicate that for some values of system parameters multiple periodic solutions appear in the form of loops and hysteresis. Finally, the average power of proposed energy harvester is given in time history diagrams for different values of nonlinear stiffness parameter and velocity of fluid flow.

Effects of nonlinear interactions of flexural modes on the performance of a beam autoparametric vibration absorber

2019 ◽  
Vol 26 (7-8) ◽  
pp. 459-474
Author(s):  
Saeed Mahmoudkhani ◽  
Hodjat Soleymani Meymand
Keyword(s):  
Frequency Response ◽  
Internal Resonance ◽  
Continuation Method ◽  
Harmonic Balance Method ◽  
Vibration Absorber ◽  
Primary System ◽  
Lumped Mass ◽  
Response Curves ◽  
Internal Resonances ◽  
The One

The performance of the cantilever beam autoparametric vibration absorber with a lumped mass attached at an arbitrary point on the beam span is investigated. The absorber would have a distinct feature that in addition to the two-to-one internal resonance, the one-to-three and one-to-five internal resonances would also occur between flexural modes of the beam by tuning the mass and position of the lumped mass. Special attention is paid on studying the effect of these resonances on increasing the effectiveness and extending the range of excitation amplitudes at which the autoparametric vibration absorber remains effective. The problem is formulated based on the third-order nonlinear Euler–Bernoulli beam theory, where the assumed-mode method is used for deriving the discretized equations of motion. The numerical continuation method is then applied to obtain the frequency response curves and detect the bifurcation points. The harmonic balance method is also employed for detecting the type of internal resonances between flexural modes by inspecting the frequency response curves corresponding to different harmonics of the response. Parametric studies on the performance of the absorber are conducted by varying the position and mass of the lumped mass, while the frequency ratio of the primary system to the first mode of the beam is kept equal to two. Results indicated that the one-to-five internal resonance is especially responsible for the considerable enhancement of the performance.

Self-powered active control of elastic and aeroelastic oscillations using piezoelectric material

2017 ◽  
Vol 28 (15) ◽  
pp. 2023-2035 ◽  
Author(s):  
Tarcísio Marinelli Pereira Silva ◽  
Carlos De Marqui
Keyword(s):  
Finite Element ◽  
Energy Harvesting ◽  
Vibration Control ◽  
The Self ◽  
Base Excitation ◽  
Sensors And Actuators ◽  
Multilayered Structures ◽  
Numerical Predictions ◽  
Active Vibration ◽  
Self Powered

Piezoelectric materials have been used as sensors and actuators in vibration control problems. Recently, the use of piezoelectric transduction in vibration-based energy harvesting has received great attention. In this article, the self-powered active vibration control of multilayered structures that contain both power generation and actuation capabilities with one piezoceramic layer for scavenging energy and sensing, another one for actuation, and a central substructure is investigated. The piezoaeroelastic finite element modeling is presented as a combination of an electromechanically coupled finite element model and an unsteady aerodynamic model. An electrical circuit that calculates the control signal based on the electrical output of the sensing piezoelectric layer and simultaneously energy harvesting capabilities is presented. The actuation energy is fully supplied by the harvested energy, which also powers active elements of the circuit. First, the numerical predictions for the self-powered active vibration attenuation of an electromechanically coupled beam under harmonic base excitation are experimentally verified. Then, the performance of the self-powered active controller is compared to the performance of a conventional active controller in another base excitation problem. Later, the self-powered active system is employed to damp flutter oscillations of a plate-like wing.

Harmonic Oscillations of Nonlinear Two-Degree-of-Freedom Systems

1955 ◽  
Vol 22 (1) ◽  
pp. 107-110
Author(s):  
T. C. Huang
Keyword(s):  
Nonlinear System ◽  
Degrees Of Freedom ◽  
Forced Oscillations ◽  
Viscous Damping ◽  
Free Oscillations ◽  
Response Curves ◽  
Harmonic Oscillations ◽  
Restoring Force ◽  
Nonlinear Restoring Force ◽  
Two Degree Of Freedom

Abstract In this paper an investigation is made of equations governing the oscillations of a nonlinear system in two degrees of freedom. Analyses of harmonic oscillations are illustrated for the cases of (1) the forced oscillations with nonlinear restoring force, damping neglected; (2) the free oscillations with nonlinear restoring force, damping neglected; and (3) the forced oscillations with nonlinear restoring force, small viscous damping considered. Amplitudes of oscillations and frequency equations are derived based on the mathematically justified perturbation method. Response curves are then plotted.

Influence of Bistable Plunge Stiffness On Nonlinear Airfoil Flutter

2021 ◽  
Author(s):  
Renan F. Corrêa ◽  
Flávio D. Marques
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Vibration ◽  
Nonlinear Behavior ◽  
Limit Cycle Oscillation ◽  
Restoring Force ◽  
Aeroelastic System ◽  
Technical Literature ◽  
Practical Applications

Abstract Aeroelastic systems have nonlinearities that provide a wide variety of complex dynamic behaviors. Nonlinear effects can be avoided in practical applications, as in instability suppression or desired, for instance, in the energy harvesting design. In the technical literature, there are surveys on nonlinear aeroelastic systems and the different manners they manifest. More recently, the bistable spring effect has been studied as an acceptable nonlinear behavior applied to mechanical vibration problems. The application of the bistable spring effect to aeroelastic problems is still not explored thoroughly. This paper contributes to analyzing the nonlinear dynamics of a typical airfoil section mounted on bistable spring support at plunging motion. The equations of motion are based on the typical aeroelastic section model with three degrees-of-freedom. Moreover, a hardening nonlinearity in pitch is also considered. A preliminary analysis of the bistable spring geometry’s influence in its restoring force and the elastic potential energy is performed. The response of the system is investigated for a set of geometrical configurations. It is possible to identify post-flutter motion regions, the so-called intrawell, and interwell. Results reveal that the transition between intrawell to interwell regions occurs smoothly, depending on the initial conditions. The bistable effect on the aeroelastic system can be advantageous in energy extraction problems due to the jump in oscillation amplitudes. Furthermore, the hardening effect in pitching motion reduces the limit cycle oscillation amplitudes and also delays the occurrence of the snap-through.

Efficient acoustic energy harvesting by deploying magnetic restoring force

2019 ◽  
Vol 28 (10) ◽  
pp. 105037 ◽  
Author(s):  
Masoud Rezaei ◽  
R Talebitooti ◽  
M I Friswell
Keyword(s):  
Energy Harvesting ◽  
Acoustic Energy ◽  
Restoring Force ◽  
Acoustic Energy Harvesting

scholarly journals Design, Construction and Evaluation of an Energy Harvesting Prototype built with Piezoelectric Materials

2020 ◽  
Author(s):  
Alejandra Echeverry Velasquez ◽  
Mateo Velez Quintana ◽  
Jose Alejandro Posada-Montoya ◽  
José Alfredo Palacio-Fernandez
Keyword(s):  
Power Generation ◽  
Energy Harvesting ◽  
Electric Power ◽  
Energy Harvester ◽  
Mechanical Load ◽  
Piezoelectric Materials ◽  
Storage System ◽  
Energy Losses ◽  
Cantilever Beams ◽  
Design Construction

The piezoelectricity allows the generation of electric power taking advantage of the movement of vehicles and pedestrians. Many prototypes have been made with piezoelectric generators, but at present, their commercialization and use has not been popularized due to their low power generation and energy losses. A design of an experimental prototype of an energy harvester with piezoelectric materials that reduces these losses and generates more energy thanks to the resonance with the beams is proposed in this article. An equilateral triangular tilde is designed such it will not deform when a force act on it. The tilde has four-cantilever beams, and it is designed to resonate with the natural frequency of the piezoelectric material. This is coupled to the piezoelectric device. The vibration generated on the beam, by average of a mechanical load, is used to generate more energy when it resonates. The piezoelectric is a ceramic material and generates a nominal power of 75 mW before placing it on the beam, and 375 mW after being placed on the beam. However, the energy collection circuit has losses due to its own consumption, the transmission of energy to the storage system, and in the mechanical system.

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