Bifurcation and chaotic vibration for an electromechanical integrated harmonic piezodrive system

In this paper, we analyzed chaotic dynamics of an electromechanical damped Duffing oscillator coupled to a rotor. The electromechanical damped device or electromechanical vibration absorber consists of an electrical system coupled magnetically to a mechanical structure (represented by the Duffing oscillator), and that works by transferring the vibration energy of the mechanical system to the electrical system. A Duffing oscillator with double-well potential is considered. Numerical simulations results are presented to demonstrate the effectiveness of the electromechanical vibration absorber. Lyapunov exponents are numerically calculated to prove the occurrence of a chaotic vibration in the non-ideal system and the suppressing of chaotic vibration in the system using the electromechanical damped device.

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Characterization of chaotic vibration without system equations

International Journal of Non-Linear Mechanics ◽

10.1016/s0020-7462(97)88305-9 ◽

1997 ◽

Vol 32 (3) ◽

pp. 547-562 ◽

Cited By ~ 1

Author(s):

Katsutoshi Yoshida ◽

Keijin Sato ◽

Sumio Yamamoto ◽

Kazutaka Yokota

Keyword(s):

Chaotic Vibration ◽

System Equations

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Chaotic Vibration of a Two-dimensional Non-strictly Hyperbolic Equation

Canadian Mathematical Bulletin ◽

10.4153/cmb-2018-012-1 ◽

2018 ◽

Vol 61 (4) ◽

pp. 768-786 ◽

Cited By ~ 1

Author(s):

Liangliang Li ◽

Jing Tian ◽

Goong Chen

Keyword(s):

Boundary Condition ◽

Boundary Conditions ◽

Hyperbolic Equation ◽

Method Of Characteristics ◽

Nonlinear Boundary ◽

Chaotic Oscillation ◽

Nonlinear Boundary Conditions ◽

Rigorous Proof ◽

Two Dimensional ◽

Chaotic Vibration

AbstractThe study of chaotic vibration for multidimensional PDEs due to nonlinear boundary conditions is challenging. In this paper, we mainly investigate the chaotic oscillation of a two-dimensional non-strictly hyperbolic equation due to an energy-injecting boundary condition and a distributed self-regulating boundary condition. By using the method of characteristics, we give a rigorous proof of the onset of the chaotic vibration phenomenon of the zD non-strictly hyperbolic equation. We have also found a regime of the parameters when the chaotic vibration phenomenon occurs. Numerical simulations are also provided.

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Energy Harvesting from Chaotic Vibration

10.26678/abcm.cobem2021.cob2021-0404 ◽

2021 ◽

Author(s):

Luã Guedes Costa ◽

Eduardo Villela Machado dos Reis ◽

Marcelo Savi

Keyword(s):

Energy Harvesting ◽

Chaotic Vibration

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Nonlinear Forced Response of Electromechanical Integrated Toroidal Drive to Coupled Excitation

The Scientific World JOURNAL ◽

10.1100/2012/743138 ◽

2012 ◽

Vol 2012 ◽

pp. 1-10

Author(s):

Lizhong Xu ◽

Fen Wang

Keyword(s):

Natural Frequencies ◽

Forced Response ◽

Drive System ◽

Mesh Stiffness ◽

Electric Excitation ◽

Time Period ◽

Electromechanical Integrated ◽

Exciting Frequency ◽

Mesh Parameter ◽

Forced Responses

The electric excitation and the parameter excitation from mesh stiffness fluctuation are analyzed. The forced response equations of the drive system to the coupled excitations are presented. For the exciting frequencies far from and near natural frequencies, the forced responses of the drive system to the coupled excitations are investigated. Results show that the nonlinear forced responses of the drive system to the coupled excitations change periodically and unsteadily; the time period of the nonlinear forced responses depends on the frequencies of the electric excitation, the mesh parameter excitation, and the nonlinear natural frequencies of the drive system; in order to improve the dynamics performance of the drive system, the frequencies of the electric excitations should not be taken as integral multiple of the mesh parameter exciting frequency.

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Multi-field coupled chaotic vibration for a micro resonant pressure sensor

Applied Mathematical Modelling ◽

10.1016/j.apm.2019.03.035 ◽

2019 ◽

Vol 72 ◽

pp. 470-485 ◽

Cited By ~ 4

Author(s):

Xiaorui Fu ◽

Lizhong Xu

Keyword(s):

Pressure Sensor ◽

Chaotic Vibration

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Coupled vibration of driving sections for an electromechanical integrated harmonic piezodrive system

AIP Advances ◽

10.1063/1.4867476 ◽

2014 ◽

Vol 4 (3) ◽

pp. 031320 ◽

Cited By ~ 9

Author(s):

Chong Li ◽

Jichun Xing ◽

Lizhong Xu

Keyword(s):

Coupled Vibration ◽

Electromechanical Integrated

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Chaotic Vibration in Aircraft Braking Systems

Volume 3A: 15th Biennial Conference on Mechanical Vibration and Noise — Vibration of Nonlinear, Random, and Time-Varying Systems ◽

10.1115/detc1995-0371 ◽

1995 ◽

Author(s):

M. Akif Özbek ◽

Steve Y. Liu ◽

James T. Gordon ◽

David S. Newman ◽

Ali R. Atilgan

Keyword(s):

Time Delay ◽

Singular System ◽

High Amplitude ◽

Vibration Modes ◽

Chaotic Vibration ◽

Chaotic Region ◽

Wide Range ◽

Amplitude Vibration ◽

Large Amplitude Vibration ◽

Model Equations

Abstract Typical vibration modes of aircraft braking systems are discussed in this paper. Special attention is given to squeal vibrations of carbon brakes. From flight tests, a wide range of response amplitudes are analyzed to determine the nature of the motion. Fourier analysis indicates the presence of a high amplitude limit cycle which seems to be initiated by a transient chaotic region. A singular system approach based on a time delay embedding confirms this finding. Time delay analysis makes it possible to contruct model equations via which intrinsic dynamics of the system can be recovered, and opens up the possibility of preventing large amplitude vibration by controlling the chaotic motion.

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