Semi-active suppression of cable 1/2-order subharmonic resonance in a cable–beam coupled system using time-delayed velocity feedback

Delay-induced dynamics of an axially moving string with direct time-delayed velocity feedback

Semi-active control on sling vibrations by the time-delayed velocity feedback with magnetorheological dampers

This paper presents the complex behavior of two-degree-of-freedom (2DOF) nonlinear coupled pitch-roll motions such as periodic, aperiodic, and chaotic solutions with or without active vibration control based on time-delayed feedback control under sinusoidal excitation. In the present study, the classical numerical integration technique has been applied to study the response behavior of coupled pitch-roll motion. A comprehensive numerical scheme based on numerical integration is applied to analyze all possible resonances of nonlinear couple pith-roll motion of the ship under time-delayed feedback. The numerical integration technique is applied to solve the nonlinear differential equation of two modes of a system model under sinusoidal harmonic excitation near the primary resonance, subharmonic resonance, combination resonance, internal resonance, and simultaneous resonance. The behavior of the system is studied using a frequency response curve and the different types of resonance cases (1) Ω ≅ ω1, (2) Ω ≅ 2ω1, ω2 ≅ 2ω1, (3) Ω ≅ ω1, ω1 ≅ ω2, (4) Ω ≅ ω1, ω2 ≅ 2ω1 are checked. The numerical simulation is carried out by numerical integration (NI) method and the results are presented graphically and are discussed. After the application of feedback control law, the frequency response plots have been obtained and control of response has been studied and compared. The different feedback control laws have been applied with either only displacement feedback with gain and delay or both displacement and velocity feedback with gain and delay. The gain and delay values are generally to be obtained from linear stability analysis. In the present study, the two-degree-of-freedom model is considered as weakly nonlinear coupled. The arbitrary gain and delay value have been used on the trial basis of different combinations of displacement and velocity gain-delay value to obtain the control of roll and pitch responses. The response stability of the 2DOF system is solved using MATLAB and Simulink toolbox. The frequency responses were analyzed using ode45 of MATLAB and Simulink of ode 45 and the results were compared. Characteristics of the solutions were also identified with the help of the phase plot diagram and Poincare map.KeywordsTime-delayed feedbackHarmonic excitationNumerical integration (NI)Poincare map

Time-delay displacement and velocity feedback of different types of active control in a cantilever beam carrying an lumped mass is investigated in this paper. Based on Euler–Bernoulli beam theory, the nonlinear governing equation is studied with damping, harmonic distribution, displacement delay, velocity delay and two time delays. The multiple scales perturbation method is applied to obtain the frequency response equations near primary, superharmonic and subharmonic resonances. A thorough study on the stability is proposed, with a particular emphasis on delay feedback. The results show that the hardening and softening behaviors of the system depend on the location of lumped mass. Furthermore, the displacement feedback gain coefficient only makes the peak amplitude move to the low frequency, yet velocity feedback coefficient and their time delays can be used to effectively enhance the stability and quench the nonlinear vibration of the cantilever beam. Thus, reasonable selection of the control system parameters can effectively improve the level of vibration control for the mechanical system.

This paper proposes the time-delayed cubic velocity feedback control strategy to improve the isolation performance of High-Static-Low-Dynamic-Stiffness (HSLDS) vibration isolator. Firstly, the primary resonance of the controlled HSLDS vibration isolator is obtained by using multiple scales method. The equivalent damping ratio and equivalent resonance frequency are defined to study the effects of feedback gain and time delay on the primary resonance. The jump phenomenon analysis of the controlled system without and with time delay is investigated by using Sylvester resultant method and optimization method, respectively. The stability analysis of the controlled system is also considered. Then, the 1/3 subharmonic resonance of the controlled system is studied by using multiple scales method. The effects of feedback gain and time delay on the 1/3 subharmonic resonance are also presented. Finally, force transmissibility is proposed to evaluate the performance of the controlled system and compared with an equivalent linear passive vibration isolator. The results show that the vibration amplitude of the controlled system around the resonance frequency region decreases and the isolation frequency band is larger compared to the equivalent one. A better isolation performance in the high frequency band can be achieved compared to the passive HSLDS vibration isolator.

Periodic solutions of a harmonically forced Duffing oscillator with time-delay state feedback are investigated using the incremental harmonic balance method. In the process of solving, the explicit effect matrix of the time delay term was derived. The stability of the periodic solutions was determined by a method which combines the continuous time approximation and multivariable Floquet theory. On this basis, the frequency–amplitude response curve and stability characteristics of the primary resonance and the 1/3 subharmonic resonance were obtained. The stable results were compared with results obtained by the numerical method, which demonstrated the effectiveness and accuracy of the incremental harmonic balance method for the analysis of strongly nonlinear equations with time delays. The influence of the time delay and feedback control parameters on the primary and 1/3 subharmonic resonance is investigated. The periodicity of the effect of the time delay is also discussed.

Resonance, stability and chaotic vibration of a quarter-car vehicle model with time-delay feedback

The time-delayed velocity and acceleration feedback control are provided to mitigate the resonances response of a nonlinear dynamic beam. By use of the method of multiple scales, the primary resonance and the 1/3 subharmonic resonance response of the controlled beam are analyzed. The excitation amplitude response peak and critical expression are obtained, and numerical simulations are also given. The effect of the feedback gains and time delayed on the steady-state response of the two types of resonances are investigated. The result show that time-delayed acceleration feedback control can effectively mitigate amplitude, and the main resonance response is affected periodically. Selecting reasonable control gain and time delay quantity can avoid the main resonance region and unstable multi-solutions, and can improve the efficiency of the vibration control.

Time-delay feedback control of a suspended cable driven by subharmonic and superharmonic resonance

Resonance and chaos of micro and nano electro mechanical resonators with time delay feedback

The subharmonic resonance response of the strongly nonlinear delay differential equation is solved using the incremental harmonic balance method. The value of the exciting frequency when the subharmonic resonance occurs is discussed. The influences of the time delay and the feedback gain on the system subharmonic resonance response are studied. The variation of the subharmonic resonance response with the system parameters is obtained. The results show that the value of the exciting frequency when the subharmonic resonance occurs is affected by the system parameters. The proportion of the one third harmonic in the amplitude increases rapidly with the increase of the exciting frequency. The variation of the amplitude ratio of the one third harmonic and the first harmonic is wavy type. The proportion of the one third harmonic in the amplitude decreases with increasing the displacement feedback gain and increases with increasing the velocity feedback gain. The proportion of the one third harmonic in the amplitude occupies a dominant position in the subharmonic resonance response.

Author Index to Volume 154 (2004)

Vibration control of a cantilever beam subject to both external and parametric excitation

In this paper, the dynamic behavior of time-delayed feedback control for maglev train system with double discrete time delays is considered with flexible guideway. Considering the maglev guideway as Beroulli-Euler beam, the mathematical model of maglev system with flexible guideway is constructed. The time delay of the two state feedback signals in the maglev system occurs simultaneously, and the values are different. The present treatment method only considers one single feedback delay, which are insufficiency. Thus, the Hopf bifurcation with double time-delay feedback of maglev train running on the flexible guideway is analyzed considering time-delayed position feedback signal τ1 and velocity feedback signal τ2. A novel method is presented to develop the double-parametric Hopf bifurcation diagram in relation to τ1 and τ2. Sufficient numerical simulations are provided to illustrate the complex dynamical behavior of the discrete delays τ1 and τ2 for maglev system and we verify the obtained theoretical analysis. Finally, the field experiments are carried out to validate the effectiveness of the Hopf bifurcation analytical method preliminarily.

Nonlinear time-delay feedback control of a suspended cable under temperature effect