Nonlinear analysis, design and vibration isolation for a bilinear system with time-delayed cubic velocity feedback

Gao, Xin; Chen, Q.

doi:10.1016/j.jsv.2013.11.009

Cited by 29 publications

(16 citation statements)

References 20 publications

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“…Abundant research results have been achieved with respect to analysis and controller design of such PWS system [10][11][12][13][14][15][16]. For instance, the stability and performance of a piecewise linear system were discussed by means of the quadratic and piecewise-quadratic Lyapunov functions which could cast as convex optimization problems and linear matrix inequalities (LMI) by Hassibi and Boyd [10].…”

Section: Introductionmentioning

confidence: 99%

“…For instance, the stability and performance of a piecewise linear system were discussed by means of the quadratic and piecewise-quadratic Lyapunov functions which could cast as convex optimization problems and linear matrix inequalities (LMI) by Hassibi and Boyd [10]. Specifically, for the discrete time piecewise affine systems, ∞ analysis and 2 Shock and Vibration was approximated by a piecewise bilinear vibration isolation system in [13]. In this work, the dynamic properties and isolation performance of this system under the time-delayed velocity feedback control were explored.…”

Section: Introductionmentioning

confidence: 99%

“…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. A famous example is presented by Hu and his coworkers [17].…”

Section: Introductionmentioning

confidence: 99%

“…∞ controller design for the piecewise linear systems based on a piecewise Lyapunov function were taken into account in [11,12]. On the other hand, it is also found that the piecewisesmooth approximation is also a powerful tool to approximate the strong nonlinear system, such as the vibration isolation system [13,14]. For example, a nonlinear system with negative stiffness was idealized by using the piecewise linear model in [15], in which numerical and analytical studies were discussed.…”

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confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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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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“…In (Leung, Guo, and Myers 2012), the periodic oscillation of the Delayed Differential Equations (DDEs) is investigated via the residue harmonic balance method and the effects of the time delayed and system parameters on the vibration frequency and amplitude are revealed. It should be noted that the isolated solutions can be found in delayed systems (Gao and Chen 2014). The search for all isolated solutions is difficult and there is a need to develop new effective methods to detect the isolated solutions.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of duffing oscillator with time delayed and/or fractional derivatives

Liao

2015

Mechanics Based Design of Structures and Machines

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The periodic motions of the fractional order and/or delayed nonlinear systems are investigated in the frequency domain using a harmonic balance method with the analytical gradients of the nonlinear quality constraints and the sensitivity information of the Fourier coefficients can also obtained. The properties of fractional order derivatives and trigonometric functions are utilized to construct the fractional order derivatives, delayed and product operational matrices. The operational matrices are used to derive the analytical formulas of nonlinear systems of algebraic equations. The stability of periodic solutions for the delayed nonlinear systems is identified by an eigenvalue analysis of quasi polynomials characteristic equations. Sensitivity analysis is performed to study the influence of the structural parameters on the system responses. Finally, Downloaded by [New York University] at 04:02 25 July 2015 2three numerical examples are presented to illustrate the validity and feasibility of the developed method. It is concluded that the proposed methodology has the potential to facilitate highly efficient optimization, as well as sensitivity and uncertainty analysis of nonlinear systems with fractional derivatives and/or time delayed.

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On artifact solutions of semi-analytic methods in nonlinear dynamics

Wagner

Lentz

2018

Arch Appl Mech

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Nonlinear dynamics is a topic of permanent interest in mechanics since decades. The authors recently published some results on a very classical topic, the dynamics of a softening Duffing oscillator under harmonic excitation focussing especially on low frequency excitation [1]. In this paper, it was shown that classical tools like Harmonic Balance and perturbation analysis may produce artificial solutions when applied without extra carefulness with respect to parameter ranges in the case of perturbation analysis or prior knowledge about the type of solution in case of Harmonic Balance. In the present paper these results are shortly summarized as they give the starting point for the additional investigations described herein. First, the method of slowly changing phase and amplitude is reviewed with respect to its capability for determining asymptotic stability of stationary solutions. It is shown, that this method can also produce artifact results when applied without extra carefulness. As next example an extended Duffing oscillator is investigated which shows, if Harmonic Balance is applied, "islands" of solutions. Using the error criterion in Harmonic Balance as described in [1] again artifact solutions can be identified.

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Nonlinear analysis, design and vibration isolation for a bilinear system with time-delayed cubic velocity feedback

Cited by 29 publications

References 20 publications

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

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

Stability analysis of duffing oscillator with time delayed and/or fractional derivatives

On artifact solutions of semi-analytic methods in nonlinear dynamics

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