Piezoelectric optimal delayed feedback control for nonlinear vibration of beams

Liu, Canchang; Yue, Shuchang; Zhou, Jianhui

doi:10.1177/0263092316628255

Cited by 27 publications

(34 citation statements)

References 31 publications

(47 reference statements)

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“…where f 11 (τ) and f 21 (τ) are the undetermined coefficients. According to the Galerkin method, substituting equations (18) and (20) into equation (15)…”

Section: (18)mentioning

confidence: 99%

“…Substituting equations (18) and (20) into equation (15) generates the subsequent equations by employing the Galerkin method:…”

Section: (18)mentioning

confidence: 99%

“…Nguyen et al [17] considered axial transporting speed as a control input and provided a fresh control algorithm for reducing the influence of transverse vibration through regulating the axial translating speed. Liu et al [18] presented an ideal deferred feedback control technique for suppressing the nonlinear vibration of an elastic beam with the actuator and piezoelectric sensor. Gong et al [19] examined the effects of feedback gains, excitation voltage, and damping on the nonlinear vibration properties and amplitude-frequency response of a nanobeam vibrational system.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Parametric Vibration and Chaotic Behaviors of an Axially Accelerating Moving Membrane

Shao

Wang

et al. 2019

Shock and Vibration

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Nonlinear vibration characteristics of a moving membrane with variable velocity have been examined. The velocity is presumed as harmonic change that takes place over uniform average speed, and the nonlinear vibration equation of the axially moving membrane is inferred according to the D’Alembert principle and the von Kármán nonlinear thin plate theory. The Galerkin method is employed for discretizing the vibration partial differential equations. However, the solutions concerning to differential equations are determined through the 4th order Runge–Kutta technique. The results of mean velocity, velocity variation amplitude, and aspect ratio on nonlinear vibration of moving membranes are emphasized. The phase-plane diagrams, time histories, bifurcation graphs, and Poincaré maps are obtained; besides that, the stability regions and chaotic regions of membranes are also obtained. This paper gives a theoretical foundation for enhancing the dynamic behavior and stability of moving membranes.

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“…where f 11 (τ) and f 21 (τ) are the undetermined coefficients. According to the Galerkin method, substituting equations (18) and (20) into equation (15)…”

Section: (18)mentioning

confidence: 99%

“…Substituting equations (18) and (20) into equation (15) generates the subsequent equations by employing the Galerkin method:…”

Section: (18)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear Parametric Vibration and Chaotic Behaviors of an Axially Accelerating Moving Membrane

Shao

Wang

et al. 2019

Shock and Vibration

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“…Beni et al 6 analyzed free vibration behavior of a single-walled carbon nanotube based on couple stress theory. Liu et al 7 applied an optimal delayed feedback control method to mitigate the nonlinear vibration of a flexible simply-simply supported beam. Hirwani et al 8 investigated transient responses of the shear deformable layered composite plate under the mechanical transverse (uniform and sinusoidal) loading by using the nonlinear finite element method.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamical behaviors of a moving membrane under external excitation

Shao

Wang

et al. 2018

Journal of Low Frequency Noise, Vibration and Active Control

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In this paper, the nonlinear vibration characteristics of a moving printing membrane under external excitation are studied. Based on the Von Karman nonlinear plate theory, the nonlinear vibration equation of the axial motion membrane under the external excitation is deduced. The Galerkin's method is used to discretize the vibration differential equations of the membrane, and then the state equation of the system is obtained. The state equation of the system is numerically solved by the fourth-order Runge-Kutta method. The relationship between the nonlinear vibration characteristics and the amplitude of external excitation, damping coefficient, and aspect ratio of the printing membrane is analyzed by using the time histories, phase-plane portraits, Poincare maps, and bifurcation diagrams. Chaotic intervals and the stable working range of the moving membrane are obtained. This study provides a theoretical basis for predicting and controlling the stability of the membrane.

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“…25,26 An optimal delayed feedback control methodology was developed to mitigate the primary and superharmonic resonances of a flexible simply-simply supported beam with a piezoelectric sensor and actuator. 27 Moon et al 28 have designed a sliding mode controller for active control of cable-stayed bridges subjected to seismic excitation. The response of an off-shore structure under random ocean waves has been controlled using a modified probabilistic neural network.…”

Section: Introductionmentioning

confidence: 99%

Feedback control for two-degree-of-freedom vibration system with fractional-order derivative damping

Liu

Zhou

et al. 2017

Journal of Low Frequency Noise, Vibration and Active Control

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A two-degree-of-freedom nonlinear vibration system of a quarter vehicle suspension system is studied by using the feedback control method considered the fractional-order derivative damping. The nonlinear dynamic model of two-degree-of-freedom vehicle suspension system is built and linear velocity and displacement controllers are used to control the nonlinear vibration of the vehicle suspension system. A case of the 1:1 internal resonance is considered. The amplitude–frequency response is obtained with the multiscale method. The asymptotic stability conditions of the nonlinear system can be gotten by using the Routh–Hurwitz criterion and the ranges of control parameters are gained in the condition of stable solutions to the system. The simulation results show that the feedback control can effectively reduce the amplitude of primary resonance, weaken or even eliminate the nonlinear vibration characteristics of the suspension system. Fractional orders have an impact on control performance, which should be considered in the control problem. The study will provide a theoretical basis and reference for the optimal design of the vehicle suspension system.

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Piezoelectric optimal delayed feedback control for nonlinear vibration of beams

Cited by 27 publications

References 31 publications

Nonlinear Parametric Vibration and Chaotic Behaviors of an Axially Accelerating Moving Membrane

Nonlinear Parametric Vibration and Chaotic Behaviors of an Axially Accelerating Moving Membrane

Nonlinear dynamical behaviors of a moving membrane under external excitation

Feedback control for two-degree-of-freedom vibration system with fractional-order derivative damping

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