scholarly journals Nonlinear Vibration Mitigation of a Beam Excited by Moving Load with Time-Delayed Velocity and Acceleration Feedback

2020 ◽  
Vol 10 (11) ◽  
pp. 3685
Author(s):  
Yiwei Tang ◽  
Jian Peng ◽  
Luxin Li ◽  
Hongxin Sun
Keyword(s):  
Feedback Control ◽  
Multiple Scales ◽  
Moving Load ◽  
Primary Resonance ◽  
Resonance Region ◽  
Excitation Amplitude ◽  
Main Resonance ◽  
Control Gain ◽  
Resonance Response ◽  
Acceleration 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.

scholarly journals Performance Analysis of an Electromagnetically Coupled Piezoelectric Energy Scavenger

Energies ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 845 ◽  
Author(s):  
Abdolreza Pasharavesh ◽  
Reza Moheimani ◽  
Hamid Dalir
Keyword(s):  
Energy Harvesting ◽  
Multiple Scales ◽  
Nonlinear Partial Differential Equations ◽  
Low Frequency ◽  
Primary Resonance ◽  
Excitation Amplitude ◽  
Load Resistance ◽  
Response Curves ◽  
Piezoelectric Energy ◽  
Resonance Frequencies

The deliberate introduction of nonlinearities is widely used as an effective technique for the bandwidth broadening of conventional linear energy harvesting devices. This approach not only results in a more uniform behavior of the output power within a wider frequency band through bending the resonance response, but also contributes to energy harvesting from low-frequency excitations by activation of superharmonic resonances. This article investigates the nonlinear dynamics of a monostable piezoelectric harvester under a self-powered electromagnetic actuation. To this end, the governing nonlinear partial differential equations of the proposed harvester are order-reduced and solved by means of the perturbation method of multiple scales. The results indicate that, according to the excitation amplitude and load resistance, different responses can be distinguished at the primary resonance. The system behavior may involve the traditional bending of response curves, Hopf bifurcations, and instability regions. Furthermore, an order-two superharmonic resonance is observed, which is activated at lower excitations in comparison to order-three conventional resonances of the Duffing-type resonator. This secondary resonance makes it possible to extract considerable amounts of power at fractions of natural frequency, which is very beneficial in micro-electro-mechanical systems (MEMS)-based harvesters with generally high resonance frequencies. The extracted power in both primary and superharmonic resonances are analytically calculated, then verified by a numerical solution where a good agreement is observed between the results.

RESONANCE RESPONSE OF A SIMPLY SUPPORTED ROTOR-MAGNETIC BEARING SYSTEM BY HARMONIC BALANCE

2012 ◽  
Vol 22 (06) ◽  
pp. 1250136 ◽  
Author(s):  
A. Y. T. LEUNG ◽  
ZHONGJIN GUO
Keyword(s):  
Harmonic Balance ◽  
Multiple Scales ◽  
Primary Resonance ◽  
Harmonic Balance Method ◽  
Magnetic Bearing ◽  
Homotopy Continuation ◽  
Response Curves ◽  
Strongly Nonlinear ◽  
Resonance Response ◽  
Strongly Nonlinear System

Both the primary and superharmonic resonance responses of a rigid rotor supported by active magnetic bearings are investigated by means of the total harmonic balance method that does not linearize the nonlinear terms so that all solution branches can be studied. Two sets of second order ordinary differential equations governing the modulation of the amplitudes of vibration in the two orthogonal directions normal to the shaft axis are derived. Primary resonance is considered by six equations and superharmonic by eight equations. These equations are solved using the polynomial homotopy continuation technique to obtain all the steady state solutions whose stability is determined by the eigenvalues of the Jacobian matrix. It is found that different shapes of frequency-response and forcing amplitude-response curves can exist. Multiple-valued solutions, jump phenomenon, saddle-node, pitchfork and Hopf bifurcations are observed analytically and verified numerically. The new contributions include the foolproof multiple solutions of the strongly nonlinear system by means of the total harmonic balance. Some predicted frequency varying amplitudes could not be obtained by the multiple scales method.

scholarly journals Time-Delayed Feedback Control of Piezoelectric Elastic Beams under Superharmonic and Subharmonic Excitations

2019 ◽  
Vol 9 (8) ◽  
pp. 1557 ◽  
Author(s):  
Jian Peng ◽  
Mingjiao Xiang ◽  
Luxin Li ◽  
Hongxin Sun ◽  
Xiuyong Wang
Keyword(s):  
Feedback Control ◽  
Elastic Beam ◽  
Delayed Feedback ◽  
Subharmonic Resonance ◽  
Delayed Feedback Control ◽  
Feedback Gain ◽  
Control Gain ◽  
Resonance Response ◽  
And Control ◽  
Time Delayed Feedback

The time-delayed displacement feedback control is provided to restrain the superharmonic and subharmonic response of the elastic support beams. The nonlinear equations of the controlled elastic beam are obtained with the help of the Euler–Bernoulli beam principle and time-delayed feedback control strategy. Based on Galerkin method, the discrete nonlinear time-delayed equations are derived. Using the multiscale method, the first-order approximate solutions and stability conditions of three superharmonic and 1/3 subharmonic resonance response on controlled beams are derived. The influence of time-delayed parameters and control gain are obtained. The results show that the time-delayed displacement feedback control can effectively suppress the superharmonic and subharmonic resonance response. Selecting reasonably the time-delayed quantity and control gain can avoid the resonance region and unstable multi-solutions and improve the efficiency of the vibration control. Furthermore, with the purpose of suppressing the amplitude peak and governing the resonance stability, appropriate feedback gain and time delay are derived.

Nonlinear Dynamics of Rotating Pretwisted Cylindrical Panels Under 1:2 Internal Resonances

2020 ◽  
Vol 30 (13) ◽  
pp. 2050191
Author(s):  
Yan Niu ◽  
Minghui Yao ◽  
Wei Zhang ◽  
Yaze Liu ◽  
Li Ma
Keyword(s):  
Multiple Scales ◽  
Strain Tensor ◽  
Shear Deformation Theory ◽  
Primary Resonance ◽  
Excitation Amplitude ◽  
Cylindrical Panel ◽  
Internal Resonances ◽  
Frequency Responses ◽  
Transverse Modes ◽  
Two Degree Of Freedom

This paper investigates the nonlinear vibrations of the rotating pretwisted cylindrical panel under higher-frequency primary resonance and lower-frequency primary resonance for the case of 1:2 internal resonances. An accurate strain-displacement relationship is derived by the Green strain tensor. First-order shear deformation theory and Hamilton principle are utilized to establish the partial differential governing equation of the rotating cylindrical panel. Galerkin approach is employed to obtain the two-degree-of-freedom nonlinear system, which contains coupling between linear stiffness terms of the two transverse modes. The method of multiple scales is used to obtain the modulation equations for the amplitudes and phases. Numerical simulations are performed to show amplitude-frequency responses and bifurcation behaviors of the system. Two types of numerical methods are compared to describe the amplitude-frequency responses of the system. The results show the accuracy of our proposed method. The effects of the detuning parameter, the damping coefficient and the excitation amplitude on amplitude-frequency responses and bifurcation behaviors are fully discussed.

scholarly journals Cubic Velocity Feedback Control of High-Amplitude Vibration of a Nonlinear Plant to a Primary Resonance Excitation

2007 ◽  
Vol 14 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Li Jun ◽  
Shen Rongying ◽  
Hua Hongxing
Keyword(s):  
Feedback Control ◽  
Multiple Scales ◽  
Primary Resonance ◽  
High Amplitude ◽  
Resonance Excitation ◽  
Feedback Gain ◽  
Response Curves ◽  
Power Requirement ◽  
Velocity Feedback ◽  
Nonlinear Plant

High-amplitude response suppression of the primary resonance of a nonlinear plant under cubic velocity feedback control is investigated. By means of the multiple scales method, two equations on the amplitude and phase of the response of the nonlinear system are obtained and the force-response and frequency-response curves are shown. The stability analyses for the open- and closed-loop responses of the system are carried out and the performance of the control strategy is investigated. The instantaneous power requirement of the control law is also examined. It can be demonstrated that appropriate choice for the feedback gain can greatly reduce the response amplitude of the primary resonance and completely eliminate the multiple responses. Finally the perturbation solutions are verified with numerical simulations.

Vibration Suppression of a Saturation Control System Using Delayed Feedback Control

2012 ◽  
Vol 226-228 ◽  
pp. 82-86
Author(s):  
Yan Ying Zhao
Keyword(s):  
Feedback Control ◽  
Analytical Solutions ◽  
Vibration Suppression ◽  
Multiple Scales ◽  
Primary Resonance ◽  
Single Mode ◽  
Original System ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Saturation Control

In the present paper, the delayed feedback control is applied to suppress the amplitude of the vibration of a beam. The method of multiple scales is employed to obtain the analytical solutions when the primary resonance and 1:2 internal resonance occur simultaneously. The predictions from analytical solutions agree with the numerical simulations well. The analytical results show that the amplitude of the beam of the saturation control is much larger than its amplitude of the single-mode motion. The effects of the delayed feedback control on amplitude of the beam are investigated when the original system is in the saturation control. There is a tunable range of the delay could be used to suppress the amplitude of the beam for a fixed value of the gain. The amplitude of the beam can be suppressed from 0.20 to 0.10 when the gain and the delay are chosen appropriate values.

Dynamics of a Duffing Oscillator With Two Time Delays in Feedback Control Under Narrow-Band Random Excitation

2008 ◽  
Vol 3 (2) ◽  
Author(s):  
Yanfei Jin ◽  
Haiyan Hu
Keyword(s):  
Feedback Control ◽  
Time Delays ◽  
Multiple Scales ◽  
Narrow Band ◽  
Duffing Oscillator ◽  
Primary Resonance ◽  
Random Excitation ◽  
Numerical Results ◽  
Linear Feedback ◽  
The Difference

The paper presents analytical and numerical results of the primary resonance of a Duffing oscillator with two distinct time delays in the linear feedback control under narrow-band random excitation. Using the method of multiple scales, the first-order and the second-order steady-state moments of the primary resonance are derived. For the case of two distinct time delays, the appropriate choices of the combinations of the feedback gains and the difference between two time delays are discussed from the viewpoint of vibration control and stability. The analytical results are in well agreement with the numerical results.

scholarly journals Dynamic Analysis of a High-Static-Low-Dynamic-Stiffness Vibration Isolator with Time-Delayed Feedback Control

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
Yong Wang ◽  
Shunming Li ◽  
Chun Cheng ◽  
Xingxing Jiang
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Multiple Scales ◽  
Dynamic Stiffness ◽  
Primary Resonance ◽  
Feedback Gain ◽  
Vibration Isolator ◽  
Controlled System ◽  
Effects Of Feedback ◽  
Isolation Performance

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.

An optimal approach in negative derivative feedback control gain synthesis

2014 ◽  
Author(s):  
Francesco Ripamonti ◽  
Flavio Cola ◽  
Ferruccio Resta
Keyword(s):  
Feedback Control ◽  
Control Gain ◽  
Optimal Approach

Nonlinear Vibrations of Two-Span Composite Laminated Plates with Equal and Unequal Subspan Lengths

2017 ◽  
Vol 9 (6) ◽  
pp. 1485-1505
Author(s):  
Lingchang Meng ◽  
Fengming Li
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Laminated Plates ◽  
Laminated Plate ◽  
Composite Laminated Plate ◽  
Vibration Localization ◽  
Composite Laminated Plates ◽  
Localization Phenomenon ◽  
Harmonic Resonance

AbstractThe nonlinear transverse vibrations of ordered and disordered two-dimensional (2D) two-span composite laminated plates are studied. Based on the von Karman's large deformation theory, the equations of motion of each-span composite laminated plate are formulated using Hamilton's principle, and the partial differential equations are discretized into nonlinear ordinary ones through the Galerkin's method. The primary resonance and 1/3 sub-harmonic resonance are investigated by using the method of multiple scales. The amplitude-frequency relations of the steady-state responses and their stability analyses in each kind of resonance are carried out. The effects of the disorder ratio and ply angle on the two different resonances are analyzed. From the numerical results, it can be concluded that disorder in the length of the two-span 2D composite laminated plate will cause the nonlinear vibration localization phenomenon, and with the increase of the disorder ratio, the vibration localization phenomenon will become more obvious. Moreover, the amplitude-frequency curves for both primary resonance and 1/3 sub-harmonic resonance obtained by the present analytical method are compared with those by the numerical integration, and satisfactory precision can be obtained for engineering applications and the results certify the correctness of the present approximately analytical solutions.

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