scholarly journals The full phase space dynamics of a magnetically levitated electromagnetic vibration harvester

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tobias Willemoes Jensen ◽  
Andrea R. Insinga ◽  
Johan Christian Ehlers ◽  
Rasmus Bjørk
Keyword(s):  
Phase Space ◽  
Permanent Magnets ◽  
Vibrational Energy ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Electrical Energy ◽  
Stable States ◽  
Damping Force ◽  
Plastic Tube ◽  
Large Power

AbstractWe consider the motion of an electromagnetic vibrational energy harvester (EMVEH) as function of the initial position and velocity and show that this displays a classical chaotic dynamical behavior. The EMVEH considered consists of three coaxial cylindrical permanent magnets and two coaxial coils. The polarities of the three magnets are chosen in such a way that the central magnet floats, with its lateral motion being prevented by enclosion in a hollow plastic tube. The motion of the floating magnet, caused by e.g. environmental vibrations, induces a current in the coils allowing electrical energy to be harvested. We analyze the behavior of the system using a numerical model employing experimentally verified expressions of the force between the magnets and the damping force between the floating magnet and the coils. We map out the phase space of the motion of the system with and without gravity, and show that this displays a fractal-like behavior and that certain driving frequencies and initial conditions allow a large power to be harvested, and that more stable states than two exists. Finally, we show that at leasts fifth order polynomial approximation is necessary to approximate the magnet-magnet force and correctly predict the system behavior.

Second Order Poincaré Map to Study Dynamical Behavior of Nonsymmetrical Gyrostat Satellite

2000 ◽  
Author(s):  
K. H. Shirazi ◽  
M. H. Ghaffari-saadat
Keyword(s):  
Phase Space ◽  
Poincaré Map ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Dynamical Behavior ◽  
Two Dimensions ◽  
Second Order ◽  
Poincare Map ◽  
Runge Kutta Method ◽  
Final Space

Abstract The second order poincare’ map is described and used for investigation of the dynamical behavior of a gyrostat satellite. The normalized attitudinal equations of motion for a typical non-symmetric gyrostat satellite are considered. For different sets of initial conditions the equations simulated by Runge-Kutta method. The poincare’ section is used to dimension reduction of system phase space. By this map the dimension reduced from six to five. Using secondary map the dimension of phase space can be reduced to four and considering symmetry of phase space the final space has two dimensions that is presentable at the plane. Bifurcation in the attitudinal behavior can be demonstrated easily by the derived map.

Experimental Research of Energy Harvesting and Storage Based on Ferroelectric Materials

2012 ◽  
Vol 476-478 ◽  
pp. 1336-1340
Author(s):  
Kai Feng Li ◽  
Rong Liu ◽  
Lin Xiang Wang
Keyword(s):  
Energy Harvesting ◽  
Electromagnetic Waves ◽  
Vibrational Energy ◽  
Waste Heat ◽  
Mechanical Strain ◽  
Electrical Potential ◽  
Electrical Energy ◽  
Ferroelectric Materials ◽  
Energy Scavenging ◽  
And Storage

The concept of energy harvesting works towards developing self-powered devices that do not require replaceable power supplies. Energy scavenging devices are designed to capture the ambient energy surrounding the electronics and convert it into usable electrical energy. A number of sources of harvestable ambient energy exist, including waste heat, vibration, electromagnetic waves, wind, flowing water, and solar energy. While each of these sources of energy can be effectively used to power remote sensors, the structural and biological communities have placed an emphasis on scavenging vibrational energy with ferroelectric materials. Ferroelectric materials have a crystalline structure that provide a unique ability to convert an applied electrical potential into a mechanical strain or vice versa. Based on the properties of the material, this paper investigates the technique of power harvesting and storage.

Behavior of a Self-Sustained Electromechanical Transducer and Routes to Chaos

2005 ◽  
Vol 128 (3) ◽  
pp. 282-293 ◽  
Author(s):  
J. C. Chedjou ◽  
K. Kyamakya ◽  
I. Moussa ◽  
H.-P. Kuchenbecker ◽  
W. Mathis
Keyword(s):  
Electronic Circuit ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Electromechanical System ◽  
Phase Portraits ◽  
Coupling Coefficients ◽  
Oscillatory Solutions ◽  
Electromechanical Transducer ◽  
Design Engineers

This paper studies the dynamics of a self-sustained electromechanical transducer. The stability of fixed points in the linear response is examined. Their local bifurcations are investigated and different types of bifurcation likely to occur are found. Conditions for the occurrence of Hopf bifurcations are derived. Harmonic oscillatory solutions are obtained in both nonresonant and resonant cases. Their stability is analyzed in the resonant case. Various bifurcation diagrams associated to the largest one-dimensional (1-D) numerical Lyapunov exponent are obtained, and it is found that chaos can appear suddenly, through period doubling, period adding, or torus breakdown. The extreme sensitivity of the electromechanical system to both initial conditions and tiny variations of the coupling coefficients is also outlined. The experimental study of̱the electromechanical system is carried out. An appropriate electronic circuit (analog simulator) is proposed for the investigation of the dynamical behavior of the electromechanical system. Correspondences are established between the coefficients of the electromechanical system model and the components of the electronic circuit. Harmonic oscillatory solutions and phase portraits are obtained experimentally. One of the most important contributions of this work is to provide a set of reliable analytical expressions (formulas) describing the electromechanical system behavior. These formulas are of great importance for design engineers as they can be used to predict the states of the electromechanical systems and respectively to avoid their destruction. The reliability of the analytical formulas is demonstrated by the very good agreement with the results obtained by both the numeric and the experimental analysis.

Phase space correspondence between Jordan and Einstein frames

2021 ◽  
pp. 2150087
Author(s):  
Amin Salehi
Keyword(s):  
Phase Space ◽  
Critical Point ◽  
Critical Points ◽  
Dynamical Behavior ◽  
Cosmological Parameters ◽  
Jordan Frame ◽  
Field Equations ◽  
Theories Of Gravity ◽  
The Stability ◽  
Jordan And Einstein Frames

Scalar–tensor theories of gravity can be formulated in the Einstein frame or in the Jordan frame (JF) which are related with each other by conformal transformations. Although the two frames describe the same physics and are equivalent, the stability of the field equations in the two frames is not the same. Here, we implement dynamical system and phase space approach as a robustness tool to investigate this issue. We concentrate on the Brans–Dicke theory in a Friedmann–Lemaitre–Robertson–Walker universe, but the results can easily be generalized. Our analysis shows that while there is a one-to-one correspondence between critical points in two frames and each critical point in one frame is mapped to its corresponds in another frame, however, stability of a critical point in one frame does not guarantee the stability in another frame. Hence, an unstable point in one frame may be mapped to a stable point in another frame. All trajectories between two critical points in phase space in one frame are different from their corresponding in other ones. This indicates that the dynamical behavior of variables and cosmological parameters is different in two frames. Hence, for those features of the study, which focus on observational measurements, we must use the JF where experimental data have their usual interpretation.

scholarly journals PIEZO BASED ELECTRIC POWER GENERATION USING 3- DIMENSIONAL MECHANICAL VIBRATIONS PRODUCED IN VEHICLES

2013 ◽  
pp. 133-138
Author(s):  
G.JITHENDRA NAIDU ◽  
K.PRANAY KUMAR REDDY ◽  
S.SIVA PRASAD
Keyword(s):  
Power Supply ◽  
Electromotive Force ◽  
Permanent Magnets ◽  
Piezoelectric Materials ◽  
Electrical Energy ◽  
Relative Displacement ◽  
Wireless Data ◽  
Magnet System ◽  
Mechanical Vibrations ◽  
Wireless Data Transmission

Due to advancement in the field of technology in recent years, wireless data transmission techniques are commonly used in electronic devices. For powering them we rely upon power supply through wires charging, else power may be supplied from batteries. But while travelling for longer distances continuously we may not be able to obtain power supply for these devices to operate or to recharge their batteries. So in order to operate them continuously we need a power source that provides continuous energy to operate these devices. The mechanical vibrations which are produced by the automobiles can be utilized as a source of energy for generating electrical energy that can be utilized by these electronic equipment to operate. These vibrations are produced by different vehicles around us which is going as a waste. This technique utilizes piezoelectric components where deformations produced by vibrations are directly converted to electrical charge via piezoelectric effect and principle of electromagnetic induction between coil and magnetic field which produces Electromotive force in the coil provided displacement to magnet by the vibrations. The piezoelectric materials and permanent magnets are used as energy conversion devices for converting mechanical vibrations to electrical energy. In this context, we introduced two methods and considered its output performance provided input vibrations, by using piezoelectric materials such as PZT for electro mechanical conversion using Mass-spring system as medium of conversion of force from vibrations applied on PZT materials and by using spring-magnet system where relative displacement of magnet with respect to coil, provided input vibrations generates Electromotive force in coil.

scholarly journals On the apparent power law in CDM halo pseudo-phase space density profiles

2017 ◽  
Vol 470 (1) ◽  
pp. 500-511 ◽  
Author(s):  
Ethan O. Nadler ◽  
S. Peng Oh ◽  
Suoqing Ji
Keyword(s):  
Phase Space ◽  
Power Law ◽  
Cold Dark Matter ◽  
Initial Conditions ◽  
Phase Space Density ◽  
Fluid Approximation ◽  
Density Profiles ◽  
Space Density ◽  
Scale Free ◽  
Hydrodynamic Calculations

Abstract We investigate the apparent power-law scaling of the pseudo-phase space density (PPSD) in cold dark matter (CDM) haloes. We study fluid collapse, using the close analogy between the gas entropy and the PPSD in the fluid approximation. Our hydrodynamic calculations allow for a precise evaluation of logarithmic derivatives. For scale-free initial conditions, entropy is a power law in Lagrangian (mass) coordinates, but not in Eulerian (radial) coordinates. The deviation from a radial power law arises from incomplete hydrostatic equilibrium (HSE), linked to bulk inflow and mass accretion, and the convergence to the asymptotic central power-law slope is very slow. For more realistic collapse, entropy is not a power law with either radius or mass due to deviations from HSE and scale-dependent initial conditions. Instead, it is a slowly rolling power law that appears approximately linear on a log–log plot. Our fluid calculations recover PPSD power-law slopes and residual amplitudes similar to N-body simulations, indicating that deviations from a power law are not numerical artefacts. In addition, we find that realistic collapse is not self-similar; scalelengths such as the shock radius and the turnaround radius are not power-law functions of time. We therefore argue that the apparent power-law PPSD cannot be used to make detailed dynamical inferences or extrapolate halo profiles inwards, and that it does not indicate any hidden integrals of motion. We also suggest that the apparent agreement between the PPSD and the asymptotic Bertschinger slope is purely coincidental.

scholarly journals Study on an Energy-Harvesting Magnetorheological Damper System in Parallel Configuration for Lightweight Battery-Operated Automobiles

Vibration ◽  
2020 ◽  
Vol 3 (3) ◽  
pp. 162-173
Author(s):  
Urvesh Kabariya ◽  
Sagil James
Keyword(s):  
Energy Harvesting ◽  
Vibrational Energy ◽  
Clean Energy ◽  
Suspension System ◽  
Comfort Level ◽  
Magnetorheological Damper ◽  
Damping Force ◽  
Secondary Systems ◽  
Parallel Configuration ◽  
Energy Dissipated

Suspension dampers are extremely critical for modern automobiles for absorbing vibrational energy while in operation. For years now, the viscous passive damper has been dominant. However, there is a constant need to improve and revolutionize the damping technology to adapt to modern road conditions and for better performance. Controlled shock absorbers capable of adapting to uneven road profiles are required to meet this challenge and enhance the passenger comfort level. Among the many types of modern damping solutions, magnetorheological (MR) dampers have gained prominence, considering their damping force control capability, fast adjustable response, and low energy consumption. Advancements in energy-harvesting technologies allow for the regeneration of a portion of energy dissipated in automotive dampers. While the amount of regenerated energy is often insufficient for regular automobiles, it could prove to be vital to support lightweight battery-operated vehicles. In battery-operated vehicles, this regenerated energy can be used for powering several secondary systems, including lighting, heating, air conditioning, and so on. This research focuses on developing a hybrid smart suspension system that combines the MR damping technology along with an electromagnetic induction (EMI)-based energy-harvesting system for applications in lightweight battery-operated vehicles. The research involves the extensive designing, numerical simulation, fabrication, and testing of the proposed smart suspension system. The development of the proposed damping system would help advance the harvesting of clean energy and enhance the performance and affordability of future battery-operated vehicles.

scholarly journals Intramolecular vibrational energy redistribution and the quantum ergodicity transition: a phase space perspective

2020 ◽  
Vol 22 (20) ◽  
pp. 11139-11173 ◽  
Author(s):  
Sourav Karmakar ◽  
Srihari Keshavamurthy
Keyword(s):  
Phase Space ◽  
Energy Flow ◽  
Vibrational Energy ◽  
Energy Redistribution ◽  
Quantum Ergodicity ◽  
Connected Network ◽  
Intramolecular Vibrational Energy Redistribution ◽  
Vibrational Energy Flow ◽  
Classical Phase Space

The onset of facile intramolecular vibrational energy flow can be related to features in the connected network of anharmonic resonances in the classical phase space.

scholarly journals Design of a 3-RPR Flexure System for Optical Switch Assembly

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Guiyue Kou ◽  
Mouyou Lin ◽  
Changbao Chu
Keyword(s):  
Permanent Magnets ◽  
Optical Switch ◽  
Low Cost ◽  
Mechanical Vibration ◽  
Analytical Models ◽  
Assembly System ◽  
Sensors And Actuators ◽  
Damping Force ◽  
Element Analysis ◽  
Compact Size

In the MEMS optical switch assembly, the collision is likely to happen between the optical fiber and the U-groove of the chip due to the uncontrollable assembly errors. However, these errors can hardly be completely eliminated by the active control using high precision sensors and actuators. It will cause the large acting force and part damage, which further leads to the assembly failure. To solve this question, this paper presents a novel low-cost three-degree-of-freedom (three-DOF) passive flexure system to adaptively eliminate the planar assembly errors. The flexure system adopts three parallel kinematic chains with a novel 3-RPR structure and has a compact size with a diameter of 125 mm and thickness of 12 mm. A novel eddy current damper with the structure of Halbach array permanent magnets (PMs) is utilized to suppress the adverse mechanical vibration of the assembly system from the background disturbances. Analytical models are established to analyze the kinematic, static, and dynamic performances of the system in detail. Finally, finite element analysis is adopted to verify the established models for optimum design. The flexure system can generate a large deformation of 1.02 mm along the two translational directions and 0.02° along the rotational direction below the yield state of the material, and it has much higher natural frequencies than 200 Hz. Moreover, the large damping force means that the designed ECD can suppress the system vibration quickly. The above results indicate the excellent characteristics of the assembly system that will be applied into the optical switch assembly.

Chaos in blood flow control in genetic and renovascular hypertensive rats

1991 ◽  
Vol 261 (3) ◽  
pp. F400-F408 ◽  
Author(s):  
K. P. Yip ◽  
N. H. Holstein-Rathlou ◽  
D. J. Marsh
Keyword(s):  
Time Series ◽  
Blood Flow ◽  
Phase Space ◽  
Renal Artery ◽  
Initial Conditions ◽  
Pressure Fluctuations ◽  
Deterministic Chaos ◽  
Tubuloglomerular Feedback ◽  
Hypertensive Rats ◽  
Statistical Measures

Hydrostatic pressure and flow in renal proximal tubules oscillate at 30–40 mHz in normotensive rats anesthetized with halothane. The oscillations originate in tubuloglomerular feedback, a mechanism that provides local blood flow regulation. Instead of oscillations, spontaneously hypertensive rats (SHR) have aperiodic tubular pressure fluctuations; the pattern is suggestive of deterministic chaos. Normal rats made hypertensive by clipping one renal artery had similar aperiodic tubular pressure fluctuations in the unclipped kidney, and the fraction of rats with irregular fluctuations increased with time after the application of the renal artery clip. Statistical measures of deterministic chaos were applied to tubular pressure data. The correlation dimension, a measure of the dimension of the phase space attractor generating the time series, indicated the presence of a low-dimension strange attractor, and the largest Lyapunov exponent, a measure of the rate of divergence in phase space, was positive, indicating sensitivity to initial conditions. These time series therefore satisfy two criteria of deterministic chaos. The measures were the same in SHR as in rats with renovascular hypertension. Since two different models of hypertension displayed similar dynamics, we suggest that chaotic behavior is a common feature of renal vascular control in the natural history of the disease.

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