scholarly journals Bifurcation, chaotic and hysteresis phenomena of broadband tristable energy harvesters

2018 ◽  
Vol 241 ◽  
pp. 01025
Author(s):  
Shengxi Zhou ◽  
Junyi Cao ◽  
Grzegorz Litak
Keyword(s):  
Multiple Solutions ◽  
Nonlinear Effects ◽  
Basins Of Attraction ◽  
Voltage Response ◽  
Mechanical Resonator ◽  
Potential Wells ◽  
Energy Harvesters ◽  
Characteristic Features ◽  
Bifurcation Chaotic ◽  
Hysteresis Phenomena

We analyze energy harvesting using a mechanical resonator with three potential wells. Nonlinear effects are leading to frequency broadband voltage response via bifurcations, multiple solutions and dynamical hysteresis. We show the characteristic features of the obtained solutions. In particular, basins of attraction of solutions are discussed.

scholarly journals Performance of broadband tristable energy harvesters

2018 ◽  
Vol 211 ◽  
pp. 05007
Author(s):  
Shengxi Zhou ◽  
Grzegorz Litak ◽  
Junyi Cao
Keyword(s):  
Spectral Analysis ◽  
Periodic Solutions ◽  
Mechanical Resonator ◽  
Potential Wells ◽  
Energy Harvesters ◽  
Voltage Output ◽  
Characteristic Features

We analyze dynamical responses of energy harvesters with a mechanical resonator possessing three potential wells. The frequency spectral analysis of simulated systems demonstrates that additional sub-harmonic and super-harmonic resonances appear. These additional solutions make the frequency broadband effect and effectively increase the voltage output. We show the characteristic features of the obtained solutions. Appearance of coexisting periodic solutions and chaotic solutions are also shortly discussed.

scholarly journals Multiple solutions of asymmetric potential bistable energy harvesters: numerical simulation and experimental validation

2019 ◽  
Author(s):  
Chris Bowen
Keyword(s):  
Multiple Solutions ◽  
Initial Conditions ◽  
High Energy ◽  
Negative Influence ◽  
Basins Of Attraction ◽  
Potential Well ◽  
Average Output ◽  
Asymmetric System ◽  
Energy Harvesters ◽  
Output Performance

In this paper we investigate the multiple solutions of nonlinear asymmetric potentialbistable energy harvesters (BEHs) under harmonic excitations. Basins of attraction under certainexcitations explain the existance of multiple solutions in the asymmetric potential BEHs and indicate that the asymmetric system has a higher probability to oscillate in the deeper potential well under low and moderate excitation levels. Thus, the appearance of asymmetric potentials in BEHs has a negative influence on the output performance. Average output powers under different excitation requencies and initial conditions illustrate that the asymmetric potential BEHs are more likely to achieve high-energy branch (HEB) with initial conditions in the shallower potential well, and the probability is influenced by the degree of asymmetry of the BEHs. Finally, experiments are carriedout, and results under constant and sweep frequency excitations demonstrate that the output performance will be actually improved for the asymmetric potential BEHs if the initial oscillations e shallower potential well

Fractal Boundary Explorations for a Nonlinear Two Degree-of-Freedom System

2012 ◽  
Author(s):  
Benjamin A. M. Owens ◽  
Brian P. Mann
Keyword(s):  
Initial Conditions ◽  
Coupled System ◽  
Basins Of Attraction ◽  
Degree Of Freedom ◽  
Fractal Boundary ◽  
Final State ◽  
Potential Wells ◽  
Mechanical Coupling ◽  
Mass Spring ◽  
Two Degree Of Freedom

This paper explores a two degree-of-freedom nonlinearly coupled system with two distinct potential wells. The system consists of a pair of linear mass-spring-dampers with a non-linear, mechanical coupling between them. This nonlinearity creates fractal boundaries for basins of attraction and forced well-escape response. The inherent uncertainty of these fractal boundaries is quantified for errors in the initial conditions and parameter space. This uncertainty relationship provides a measure of the final state and transient sensitivity of the system.

scholarly journals Multiple solutions and transient chaos in a nonlinear flexible coupling model

2021 ◽  
Vol 43 (10) ◽  
Author(s):  
Jerzy Margielewicz ◽  
Damian Gąska ◽  
Tadeusz Opasiak ◽  
Grzegorz Litak
Keyword(s):  
Periodic Solutions ◽  
Multiple Solutions ◽  
Computer Modelling ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Coupling Model ◽  
Basins Of Attraction ◽  
Largest Lyapunov Exponent ◽  
Transient Chaos ◽  
Stable Periodic

AbstractThis paper investigates the nonlinear dynamics of a flexible tyre coupling via computer modelling and simulation. The research mainly focused on identifying basins of attraction of coexisting solutions of the formulated phenomenological coupling model. On the basis of the derived mathematical model, and by assuming ranges of variability of the control parameters, the areas in which chaotic clutch movement takes place are determined. To identify multiple solutions, a new diagram of solutions (DS) was used, illustrating the number of coexisting solutions and their periodicity. The DS diagram was drawn based on the fixed points of the Poincaré section. To verify the proposed method of identifying periodic solutions, the graphic image of the DS was compared to the three-dimensional distribution of the largest Lyapunov exponent and the bifurcation diagram. For selected values of the control parameter ω, coexisting periodic solutions were identified, and basins of attraction were plotted. Basins of attraction were determined in relation to examples of coexistence of periodic solutions and transient chaos. Areas of initial conditions that correspond to the phenomenon of unstable chaos are mixed with the conditions of a stable periodic solution, to which the transient chaos is attracted. In the graphic images of the basins of attraction, the areas corresponding to the transient and periodic chaos are blurred.

scholarly journals On the New Nonlinear Properties of the Nonlinear Heat Conductivity Problem

2019 ◽  
Vol 9 (1) ◽  
pp. 1542-1543
Keyword(s):  
Thermal Conductivity ◽  
Exact Analytical Solution ◽  
Thermal Structure ◽  
Nonlinear Effects ◽  
Spatial Localization ◽  
Thermal Processes ◽  
Nonlinear Media ◽  
Nonlinear Properties ◽  
Characteristic Features ◽  
Nonlinear Thermal Conductivity

In this article, we discuss one problem of nonlinear thermal conductivity with double nonlinearity; an exact analytical solution has been found for it, the analysis of which allows revealing a number of characteristic features of thermal processes in nonlinear media. The following nonlinear effects have been established: the inertial effect, the finite propagation velocity of thermal disturbances, the spatial localization of heat, and the effect of the finite time of the existence of a thermal structure in an absorption medium.

Tristable Energy Harvesters With Asymmetric Potential Wells: Analytical Study

2017 ◽  
Author(s):  
Shengxi Zhou ◽  
Lei Zuo
Keyword(s):  
Energy Harvesting ◽  
High Energy ◽  
Harmonic Excitation ◽  
Potential Wells ◽  
Potential Barriers ◽  
Energy Harvesters ◽  
Response Characteristics ◽  
The Stability ◽  
Excitation Conditions ◽  
Main Factor

In order to reveal the nonlinear response characteristics of asymmetric tristable energy harvesters, this paper originally deduces their complete harmonic balance solutions. In addition, the Jacobian matrix for determining the stability of these analytical solutions is presented. Under different harmonic excitation conditions, the multi-solution response characteristics of asymmetric tristable energy harvesters are analyzed. In detail, asymmetric tristable energy harvesters are found to have seven solutions (four stable solutions) under the appropriate excitation condition. The influence mechanism of asymmetry of potential wells on tristable energy harvesting performance is studied. The results show that the potential barrier is a main factor to influence high-energy interwell oscillation orbit height, which determines the output voltage amplitude and the overall energy harvesting performance. The influence essence of asymmetry for tristable energy harvesters is to change their potential wells and adjust the distribution of their potential barriers.

Influence of Piezoelectric Energy Transfer on the Interwell Oscillations of Multistable Vibration Energy Harvesters

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Aravind Kumar ◽  
Shaikh Faruque Ali ◽  
A. Arockiarajan
Keyword(s):  
Energy Transfer ◽  
Electrical Energy ◽  
Potential Energy Function ◽  
Load Resistance ◽  
Theoretic Analysis ◽  
Mechanical Oscillator ◽  
Potential Wells ◽  
Energy Harvesters ◽  
Piezoelectric Energy ◽  
Electromechanical Energy

This manuscript investigates the effect of nonconservative electromechanical energy transfer on the onset of interwell motions in multistable piezoelectric energy harvesters. Multistable piezoelectric energy harvesters have been proven to outperform their linear counterparts when they undergo interwell oscillations. The conditions for interwell oscillations in such harvesters are generally characterized in terms of their potential energy function. This is accurate for a stand-alone mechanical oscillator but when the piezoelectric patches and a load resistance are included, a part of the kinetic energy supplied to the system is converted into electrical energy. In this manuscript, the Melnikov necessary conditions for interwell oscillations are derived, considering the effect of this nonconservative piezoelectric energy transfer. Through Melnikov theoretic analysis, it is shown that in a tristable harvester with all the three potential wells having the same depth, a higher excitation level is required to enable exits from the middle well to the outer wells when compared to the exits from the outer wells to the middle well. This is in stark contrast to a stand-alone tristable mechanical oscillator wherein interwell motions are simultaneously enabled for all the wells having the same depth.

Quantitative analysis of the heterogeneous population of endocytic vesicles

2017 ◽  
Vol 15 (02) ◽  
pp. 1750008 ◽  
Author(s):  
Konstantin Kozlov ◽  
Vera Kosheverova ◽  
Rimma Kamentseva ◽  
Marianna Kharchenko ◽  
Alena Sokolkova ◽  
...  
Keyword(s):  
Dynamical Behavior ◽  
Growth Factor Receptor ◽  
Basins Of Attraction ◽  
Endocytic Vesicle ◽  
Biological Images ◽  
Segmentation Methods ◽  
Characteristic Features ◽  
Object Shapes ◽  
Opening And Closing ◽  
Endocytic Vesicles

The quantitative characterization of endocytic vesicles in images acquired with microscope is critically important for deciphering of endocytosis mechanisms. Image segmentation is the most important step of quantitative image analysis. In spite of availability of many segmentation methods, the accurate segmentation is challenging when the images are heterogeneous with respect to object shapes and signal intensities what is typical for images of endocytic vesicles. We present a Morphological reconstruction and Contrast mapping segmentation method (MrComas) for the segmentation of the endocytic vesicle population that copes with the heterogeneity in their shape and intensity. The method uses morphological opening and closing by reconstruction in the vicinity of local minima and maxima respectively thus creating the strong contrast between their basins of attraction. As a consequence, the intensity is flattened within the objects and their edges are enhanced. The method accurately recovered quantitative characteristics of synthetic images that preserve characteristic features of the endocytic vesicle population. In benchmarks and quantitative comparisons with two other popular segmentation methods, namely manual thresholding and Squash plugin, MrComas shows the best segmentation results on real biological images of EGFR (Epidermal Growth Factor Receptor) endocytosis. As a proof of feasibility, the method was applied to quantify the dynamical behavior of Early Endosomal Autoantigen 1 (EEA1)-positive endosome subpopulations during EGF-stimulated endocytosis.

Modeling of Piezoelectric Energy Harvesting from an L-shaped Beam-mass Structure with an Application to UAVs

2008 ◽  
Vol 20 (5) ◽  
pp. 529-544 ◽  
Author(s):  
Alper Erturk ◽  
Jamil M. Renno ◽  
Daniel J. Inman
Keyword(s):  
Energy Harvesting ◽  
Energy Harvester ◽  
Electrical Power ◽  
Distributed Parameter ◽  
Voltage Response ◽  
Shaped Beam ◽  
Energy Harvesters ◽  
Piezoelectric Energy ◽  
Distributed Parameter Model

Cantilevered piezoelectric energy harvesters have been extensively investigated in the literature of energy harvesting. As an alternative to conventional cantilevered beams, this article presents the L-shaped beam-mass structure as a new piezoelectric energy harvester configuration. This structure can be tuned to have the first two natural frequencies relatively close to each other, resulting in the possibility of a broader band energy harvesting system. This article describes the important features of the L-shaped piezoelectric energy harvester configuration and develops a linear distributed parameter model for predicting the electromechanically coupled voltage response and displacement response of the harvester structure. After deriving the coupled distributed parameter model, a case study is presented to investigate the electrical power generation performance of the L-shaped energy harvester. A direct application of the L-shaped piezoelectric energy harvester configuration is proposed for use as landing gears in unmanned air vehicle applications and a case study is presented where the results of the L-shaped — energy harvester — landing gear are favorably compared against the published experimental results of a curved beam configuration used for the same purpose.

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