Dynamical properties of a forced vibration isolation system with real-power nonlinearities in restoring and damping forces

Huang, Dongmei; Xu, Wei; Xie, Wen-Xian; Liu, Yajuan

doi:10.1007/s11071-015-2016-2

Cited by 30 publications

(16 citation statements)

References 25 publications

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“…However, many materials whose elastic deformations cannot be exactly, described as a polynomial [2,3]. In these materials, the force-deflection relationship includes non-integer exponents of a fractional order [2][3][4][5][6][7][8][9]. Specifically, the nonlinear materials of Ramberg-Osgood type, which have been applied to depict the elastic properties of the aircraft materials such as aluminum and titanium [4].…”

Section: Introductionmentioning

confidence: 99%

“…The method of multiple scales was improved to cover the cases in which the nonlinearity is not necessarily small. Huang et al [9] utilized the time-delayed cubic velocity feedback to improve the performance of a vibration isolation system whose restoring and damping forces are in a real-power form. They also studied the primary resonance, dynamic stability and transmissibility for this system under base excitation using the method of multiple scales.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, the PPF controller is utilized to suppress the primary resonance vibrations of the base excited oscillator with real-power exponents in the restoring and damping forces given [9]. This oscillator is harmonically excited on its base.…”

Section: Introductionmentioning

confidence: 99%

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Utilizing the time delayed PPF controller to suppress vibrations of a nonlinear system containing real power exponents in damping and restoring forces

Abdelhafez¹

2019

J. vibroeng.

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The time delayed Positive Position Feedback (PPF) controller is utilized to suppress the primary resonance of vibrations of an excited base oscillator by real power exponents of the restoring and damping forces. Multiple scales method is conducted to get the frequency response equations. The stability of the system is studied by using the Lyapunov first method. The influences of system parameters and time delay on the system response are investigated to avoid the jump phenomenon for better system performance. Time margin is deduced for most possible values of controller gain. Analytic results are verified by numerical integration of the original system equations.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Utilizing the time delayed PPF controller to suppress vibrations of a nonlinear system containing real power exponents in damping and restoring forces

Abdelhafez¹

2019

J. vibroeng.

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“…In fact, time delay can be caused by finite signal transmission speeds and memory effects [17][18][19][20][21][22][23], the physical properties of the equipment used for control and transport delay, and filtering and processing data [21]. Time-delayed feedback control is a powerful tool for achieving a wide range of operating regimes and enhancing amplitude-frequency characteristics [13,14,16]; the utilization of time delay has developed for many years in vibration engineering fields.…”

Section: Introductionmentioning

confidence: 99%

“…Then, a time delay position feedback controller to reduce the sway of container cranes was put forward in [23]. Recently, the abundant dynamic properties which exist in a vibration isolation system under delayed feedback control were discussed in detail in [22]. Nevertheless, the stochastic dynamics of the piecewise-smooth structure with negative stiffness under delayed feedback control, which is prone unstable in the dynamic excitations, have not been reported in the literature.…”

Section: Introductionmentioning

confidence: 99%

Vibration Analysis of a Piecewise-Smooth System with Negative Stiffness under Delayed Feedback Control

Huang

Yang

et al. 2017

Shock and Vibration

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The principal resonance of a delayed piecewise-smooth (DPWS) system with negative stiffness under narrow-band random excitation is investigated in aspects of multiscale analysis, design methodology of the controller, and response properties. The amplitude-frequency response and steady-state moments together with the corresponding stability conditions of the controlled stochastic system are derived, in which the degradation case is also under consideration. Then, from the perspective of the equivalent damping, the comparisons of the response characteristics of the controlled system to the uncontrolled system, such as the phenomenon of frequency island, are fulfilled. Furthermore, sensitivity of the system response to feedback gain and time delay is studied and interesting dynamic properties are found. Meanwhile, the classification of the steady-state solution is also discussed. To control the maximum amplitude, the feedback parameters are determined by the frequency response together with stability boundaries which must be utilized to exclude the combinations of the unstable parameters. For the case with small noise intensity, mean-square responses present the similar characteristics to what is discussed in the deterministic case.

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Dynamical analysis of an SDOF quasi‐linear system with jump noises and multitime‐delayed feedback forces

Jia

Luo

Hao

et al. 2022

Int Journal of Mech Sys Dyn

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In this paper, stochastic dynamics of a single degree-of-freedom quasi-linear system with multitime delays and Poisson white noises are investigated using an approximate procedure based on the stochastic averaging method. The simplified equations, including the averaged stochastic differential equation and the averaged generalized Fokker-Planck-Kolmogorov equation, are obtained to calculate the probability density functions (PDFs) to explore stationary responses.The expression of the Lyapunov exponent is presented to examine the asymptotic stochastic Lyapunov stability. An illustrative example of a quasi-linear oscillator with two Poisson white noises controlled by two time-delayed feedback forces is worked out to demonstrate the validity of the proposed method. The approximate stationary PDFs of stochastic responses and asymptotic stochastic stability are demonstrated numerically and theoretically. The results show that the Gaussian white noise has a stronger influence on the dynamics than the Poisson white noise with a small mean arrival rate. Moreover, the influence of the time delay and noise parameters on stochastic dynamics is investigated. It is found that the PDFs under the Poisson white noise approach those under Gaussian white noise as the mean arrival rate increases. The time delay can induce stochastic P-bifurcation of the system. It is also found that the increase of time delay and the mean arrival rates of the Poisson white noises will broaden the unstable parameter region. The comparison between numerical and theoretical results shows the effectiveness of the proposed method.time delay, stochastic response and stability, Poisson white noise | INTRODUCTIONTime delay can be experienced in many applications and fields, such as power, electronic technology, network, and transportation systems. The existence of time delay significantly affects the system behavior, especially for enormous nonlinear engineering structures. 1-3 For example, time delay in feedback control systems cannot be avoided because it takes time to detect the system state, calculate the control force, and transfer the control signal from the computer to the actuator. Time delay does not only affect the control effect but can cause

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Dynamical properties of a forced vibration isolation system with real-power nonlinearities in restoring and damping forces

Cited by 30 publications

References 25 publications

Utilizing the time delayed PPF controller to suppress vibrations of a nonlinear system containing real power exponents in damping and restoring forces

Utilizing the time delayed PPF controller to suppress vibrations of a nonlinear system containing real power exponents in damping and restoring forces

Vibration Analysis of a Piecewise-Smooth System with Negative Stiffness under Delayed Feedback Control

Dynamical analysis of an SDOF quasi‐linear system with jump noises and multitime‐delayed feedback forces

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