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

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 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.

Potential Well Escape of an Eccentric Disk

2012 ◽  
Author(s):  
Genevieve M. Lipp ◽  
Brian P. Mann
Keyword(s):  
Initial Conditions ◽  
Equations Of Motion ◽  
Basins Of Attraction ◽  
Potential Well ◽  
Mass Approximation ◽  
Amplitude Parameter ◽  
Related Point ◽  
Eccentric Disk ◽  
Disk Rolling ◽  
Cubic Function

This paper investigates the dynamic behavior of an eccentric disk rolling on a curve of arbitrary shape and then on a curve defined as a cubic function. Comparisons are made to a disk with no eccentricity and the related point mass approximation. The curve is subject to base excitation, and the system is considered from the perspective of a potential well problem where escape is possible on one side. The equations of motion are derived using a roll-without-slip constraint, and the behavior is investigated by means of simulated frequency and amplitude parameter sweeps and by considering the basins of attraction when initial conditions or forcing parameters are varied.

The possibility of a kind of Bose particle to obtain high energy and superradiance

2020 ◽  
Author(s):  
Wen-Xiang Chen
Keyword(s):  
High Energy ◽  
Potential Well ◽  
Maximum Value

When \Delta x \Delta p < \hbar / 2 happens at the same time when the entropy reaches its maximum value, the boson will condense, and if there is a potential well but it does not explode, then the boson will gain high energy (more than normal).This article is to illustrate the possibility of a kind of Bose particle to obtain high energy.

Digestibility of nutrients and milk productivity of cows when using the concentrate mixture with the inclusion of rapeseed presscake

2020 ◽  
pp. 48-53
Author(s):  
L. Yarmots ◽  
G. Yarmots ◽  
A. Belenkaya
Keyword(s):  
Protein Digestibility ◽  
High Energy ◽  
Negative Influence ◽  
The Body ◽  
Milk Productivity ◽  
Lactating Cows ◽  
Low Protein ◽  
Concentrate Mixture ◽  
Almost All ◽  
Experimental Group

For ruminants, especially high-yielding animals in addition to the complete supply of animals with protein, its digestibility in the rumen is important. With low protein digestibility in the rumen, the released ammonia will be more effectively used by the rumen microflora, and the undigestible protein in the subsequent sections of the digestive tract can serve as a source of amino acids for the body. The use of concentrate mixtures with the inclusion of local, affordable and cheaper grain feeds, in particular a high-energy and protein ingredient- rapeseed presscake makes it possible to increase the milk productivity of cows throughout lactation. These presscakes are well balanced in their amino acid composition and belong to feeds whose protein has a low degree of digestibility in the rumen. The purpose of the researches was to study the digestibility of nutrients and milk productivity of cows when using the concentrate mixture with the inclusion of rapeseed presscake. In the scientific and economic experiment has been carried out on lactating cows, where the cows of the experimental group in the concentrate mixture of peas has been replaced with rapeseed presscake the digestibility of nutrients in the ration, energy metabolism and milk productivity have been studied. Studies have shown that almost all the nutrients were significantly better digested by the animals of the experimental group. Energy in milk was more allocated by cows of the experimental group by 6,29 MJ. From cows of the experimental group for 100 and 305 days of lactation has been obtained more milk by 6,27 and 7,06 %, respectively, than from control herdmates. The biochemical parameters of blood were within the limits of the physiological norm in animals of both groups. Thus, the replacement of peas with rapeseed presscake in the concentrate mixture did not have a negative influence on the metabolic processes and helped to increase the milk productivity of cows.

BASIN CONFIGURATION OF A SIX-DIMENSIONAL MODEL OF AN ELECTRIC POWER SYSTEM

2002 ◽  
Vol 12 (06) ◽  
pp. 1333-1356 ◽  
Author(s):  
YOSHISUKE UEDA ◽  
HIROYUKI AMANO ◽  
RALPH H. ABRAHAM ◽  
H. BRUCE STEWART
Keyword(s):  
Power Systems ◽  
Power System ◽  
Initial Conditions ◽  
Electrical Power ◽  
Practical Importance ◽  
Intervention Strategy ◽  
Basins Of Attraction ◽  
Electric Power System ◽  
Point Of View ◽  
Electrical Power System

As part of an ongoing project on the stability of massively complex electrical power systems, we discuss the global geometric structure of contacts among the basins of attraction of a six-dimensional dynamical system. This system represents a simple model of an electrical power system involving three machines and an infinite bus. Apart from the possible occurrence of attractors representing pathological states, the contacts between the basins have a practical importance, from the point of view of the operation of a real electrical power system. With the aid of a global map of basins, one could hope to design an intervention strategy to boot the power system back into its normal state. Our method involves taking two-dimensional sections of the six-dimensional state space, and then determining the basins directly by numerical simulation from a dense grid of initial conditions. The relations among all the basins are given for a specific numerical example, that is, choosing particular values for the parameters in our model.

3D Printing — The Basins of Tristability in the Lorenz System

2017 ◽  
Vol 27 (08) ◽  
pp. 1750128 ◽  
Author(s):  
Anda Xiong ◽  
Julien C. Sprott ◽  
Jingxuan Lyu ◽  
Xilu Wang
Keyword(s):  
Lorenz System ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Basins Of Attraction ◽  
Symmetric Pair ◽  
State Space Approach ◽  
3D Printers ◽  
The Lorenz System ◽  
Almost All ◽  
Space Approach

The famous Lorenz system is studied and analyzed for a particular set of parameters originally proposed by Lorenz. With those parameters, the system has a single globally attracting strange attractor, meaning that almost all initial conditions in its 3D state space approach the attractor as time advances. However, with a slight change in one of the parameters, the chaotic attractor coexists with a symmetric pair of stable equilibrium points, and the resulting tri-stable system has three intertwined basins of attraction. The advent of 3D printers now makes it possible to visualize the topology of such basins of attraction as the results presented here illustrate.

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.

Theoretical Analysis and General Characteristics for Nonlinear Vibration Energy Harvesters

2021 ◽  
Author(s):  
Hanxiao Wu ◽  
Zhi Tao ◽  
Haiwang Li ◽  
Tiantong Xu ◽  
Wenbin Wang ◽  
...  
Keyword(s):  
Output Power ◽  
Numerical Study ◽  
Power Line ◽  
Energy Harvesters ◽  
Output Performance ◽  
Equivalent Time ◽  
Time Average ◽  
Mechanical Damping ◽  
Limit Power ◽  
Nonlinear Energy

Abstract In this paper, we present a systematic theoretical and numerical study of the output performance of nonlinear energy harvesters. The general analytical expression of output power for systems with different combinations of nonlinear stiffness and nonlinear damping, as well as symmetrical and asymmetrical systems, have been derived based on harmonic balance method, observing compliance with numerical results. We theoretically prove that there is a limit power for all nonlinear systems which is determined exclusively by the vibrator mass, excitation acceleration, and mechanical damping. The results also indicate that for symmetrical stiffness systems, the asymmetrical damping components have no effect on the output performance. Additionally, we derived semi-analytical solutions of the matching loads and numerically investigated the influence of nonlinear coefficients on the output power with matched load. When the load matches device parameters and is much larger than the internal resistance, the equivalent time-average damping is equal to the mechanical damping. Although the matching load and output power vary with the nonlinear coefficients, the normalized power and matching resistance ratio follow a power function, named matching power line, which is independent of the structural parameters. With the improvement of the equivalent time-average short-circuit damping in the vibration range, the normalized power moves to the right end of the matching power line, and the output power approach to the limit power. These conclusions provide general characteristics of nonlinear energy harvesters, which can be used to guide the design and optimization of energy harvesters.

Sign in / Sign up

Export Citation Format

Share Document