scholarly journals The Vibration reduction of a cantilever beam subjected to parametric excitation using time delay feedback

2017 ◽  
Vol 13 (2) ◽  
pp. 7186-7193
Author(s):  
Y A Amer
Keyword(s):  
Time Delay ◽  
Cantilever Beam ◽  
Parametric Excitation ◽  
Order Approximation ◽  
Perturbation Technique ◽  
Dynamical Behavior ◽  
Multiple Scale ◽  
Steady State Solution ◽  
State Feedback Control ◽  
Resonance Case

In this paper, dynamical behavior of a cantilever beam subject to parametric excitation under state feedback control with time delay is analyzed. The method of multiple scale perturbation technique is applied to obtain the solution up to the first order approximation. We obtain equations for the amplitude and phase. We studied all resonance cases numerically. Stability of the steady state solution for the selected resonance case is studied applying Rung-Kutta fourth method and frequency response equation via Matlab 7.0 and maple 16. From the results, it can be seen that the frequency and amplitude responses for the selected resonance case can be affected by the time delayed control. Effects of different parameters of the system are studied.

scholarly journals Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback

2006 ◽  
Vol 13 (2) ◽  
pp. 65-83 ◽  
Author(s):  
A.F. EL-Bassiouny
Keyword(s):  
Time Delay ◽  
State Feedback ◽  
Order Approximation ◽  
Perturbation Technique ◽  
Multiple Scale ◽  
State Feedback Control ◽  
Response Curves ◽  
Equivalent Damping ◽  
Scale Perturbation ◽  
First Order Approximation

Time delays occur in many physical systems. In particular, when automatic control is used with structural or mechanical systems, there exists a delay between measurement of the system state and corrective action. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. We investigate the fundamental resonance and subharmonic resonance of order one-half of a harmonically oscillation under state feedback control with a time delay. By using the multiple scale perturbation technique, the first order approximation of the resonances are derived and the effect of time delay on the resonances is investigated. The fixed points correspond to a periodic motion for the starting system and we show the external excitation-response and frequency-response curves. We analyze the effect of time delay and the other different parameters on these oscillations.

Application of Time-Delay Absorber to Suppress Vibration of a Dynamical System to Tuned Excitation

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
W. A. A. El-Ganaini ◽  
H. A. El-Gohary
Keyword(s):  
Dynamical System ◽  
Time Delay ◽  
Cantilever Beam ◽  
Resonance Condition ◽  
Order Approximation ◽  
Nonlinear Differential Equations ◽  
Multiple Time ◽  
Control Input ◽  
Resonance Case ◽  
System Behavior

In this work, we present a comprehensive investigation of the time delay absorber effects on the control of a dynamical system represented by a cantilever beam subjected to tuned excitation forces. Cantilever beam is one of the most widely used system in too many engineering applications, such as mechanical and civil engineering. The main aim of this work is to control the vibration of the beam at simultaneous internal and combined resonance condition, as it is the worst resonance case. Control is conducted via time delay absorber to suppress chaotic vibrations. Time delays often appear in many control systems in the state, in the control input, or in the measurements. Time delay commonly exists in various engineering, biological, and economical systems because of the finite speed of the information processing. It is a source of performance degradation and instability. Multiple time scale perturbation method is applied to obtain a first order approximation for the nonlinear differential equations describing the system behavior. The different resonance cases are reported and studied numerically. The stability of the steady-state solution at the selected worst resonance case is investigated applying Runge–Kutta fourth order method and frequency response equations via Matlab 7.0 and Maple11. Time delay absorber is effective, but within a specified range of time delay. It is the critical factor in selecting such absorber. Time delay absorber is better than the ordinary one as from the effectiveness point of view. The effects of the different absorber parameters on the system behavior and stability are studied numerically. A comparison with the available published work showed a close agreement with some previously published work.

scholarly journals Vibration Control in MEMS Resonator Using Positive Position Feedback (PPF) Controller

2016 ◽  
Vol 12 (11) ◽  
pp. 6821-6834
Author(s):  
Y A Amer ◽  
A.T EL Sayed ◽  
A.M. Salem
Keyword(s):  
Order Approximation ◽  
Perturbation Technique ◽  
Multiple Scale ◽  
Steady State Solution ◽  
Positive Position Feedback ◽  
Mems Resonator ◽  
Position Feedback ◽  
Resonator System ◽  
The Stability ◽  
First Order Approximation

In this paper, the vibration of a micro-electromechanical resonator with positive position feedback controller is studied. The analytical results are obtained to the first order approximation by using the multiple scale perturbation technique. The stability of the steady-state solution is presented and studied applying frequency response equations near the simultaneous primary and internal resonance cases. The effects of the controller and some system parameters on the vibrating system are studied numerically. The main result of this paper indicates that it is possible to reduce the vibration for the resonator system.

Nonlinear Stability Considerations in Thermoelastic Contact

1999 ◽  
Vol 66 (1) ◽  
pp. 109-116 ◽  
Author(s):  
J. A. Pelesko
Keyword(s):  
Steady State ◽  
Perturbation Technique ◽  
Multiple Scale ◽  
Steady State Solution ◽  
Rigid Wall ◽  
Stable Steady State ◽  
Dynamic Information ◽  
Multiple Steady State ◽  
Singular Perturbation Technique ◽  
Steady State Solutions

The behavior of a one-dimensional thermoelastic rod is modeled and analyzed. The rod is held fixed and at constant temperature at one end, while at the other end it is free to separate from or make contact with a rigid wall. At this free end a pressure and gap-dependent thermal boundary condition is imposed which couples the thermal and elastic problems. Such systems have previously been shown to undergo a bifurcation from a unique linearly stable steady-state solution to multiple steady-state solutions with alternating stability. Here, the system is studied using a two-timing or multiple-scale singular perturbation technique. In this manner, the analysis is extended into the nonlinear regime and dynamic information about the history dependence and temporal evolution of the solution is obtained.

Vibration Suppression of Subharmonic Resonance Response Using a Nonlinear Vibration Absorber

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
A. T. EL-Sayed ◽  
H. S. Bauomy
Keyword(s):  
Nonlinear System ◽  
Vibration Suppression ◽  
Order Approximation ◽  
Perturbation Technique ◽  
Multiple Scale ◽  
Internal Resonances ◽  
State Response ◽  
Averaged Equations ◽  
Resonance Response ◽  
Scale Perturbation

This paper is concerned with the vibration of a two degree-of-freedom (2DOF) nonlinear system subjected to multiparametric excitation forces. The vibrating motion of the system is described by the coupled differential equations having both quadratic and cubic terms. The aim of this work is to use a nonlinear absorber to control the vibration of the nonlinear system near the simultaneous subharmonic and internal resonances, where the vibrations are severe. Multiple scale perturbation technique (MSPT) is applied to obtain the averaged equations up to the second-order approximation. The steady-state response and their stability are studied numerically for the nonlinear system at the simultaneous subharmonic and internal resonances. Some recommendations regarding to the different system parameters are given following studying the effects of various parameters. Comparison with the available published work is made.

scholarly journals Positive Position Feedback Controllers for Reduction the Vibration of a Nonlinear Spring Pendulum

2016 ◽  
Vol 12 (11) ◽  
pp. 6758-6772
Author(s):  
Y a Amer
Keyword(s):  
Perturbation Technique ◽  
Multiple Scale ◽  
Resonance Case ◽  
Feedback Controllers ◽  
Pendulum System ◽  
Nonlinear Spring ◽  
Positive Position Feedback ◽  
Position Feedback ◽  
Scale Perturbation ◽  
The Stability

In this paper, the two positive position feedback controllers (PPF) are proposed to reduce the longitudinal and angular vibrations of the nonlinear spring pendulum system which simulated the ship roll motion. This described by a four-degreeof- freedom system (4-DOF) which subjected to the external excitation force at simultaneous primary and internal resonance case. The method of multiple scale perturbation technique (MSPT) is applied to study the approximate solution of the given system. The stability of the system is investigated near the resonance case applying the frequency-response equations. Numerically, the effects of different controllers parameters on the basic system behavior are studied.

scholarly journals Active and Time Delay Controls on Vibrations of the Micro-Electro-Mechanical System (MEMS) Resonator

2019 ◽  
pp. 1-17
Author(s):  
Y. A. Amer ◽  
A. T. El-Sayed ◽  
F. O. Darwesh
Keyword(s):  
Time Delay ◽  
Numerical Solution ◽  
Mechanical System ◽  
Perturbation Technique ◽  
Primary Resonance ◽  
Multiple Scale ◽  
Micro Electro Mechanical System ◽  
Mems Resonator ◽  
Response Equation ◽  
The Stability

In this paper, the active control and time delay control are applied on a nonlinear mechanical system subjected to external force to reduce the resulted vibration. The system is modeled by a unique nonlinear differential equation. The multiple scale perturbation technique (MSPT) was applied to obtain an approximate solution and showing the response equation. The stability of the system at primary resonance case is investigated using both of phase plane and frequency response equation. Numerical solution is obtained using Runge – Kutta forth order method.Also, MATLAB 14.0 and Maple 18.0 programs were used to study the numerical solution and the effect of the different parameters for the response of the nonlinear dynamic mechanical system.

scholarly journals On an Impulsive Food Web System with Mutual Interference and Distributed Time Delay

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Zhen Wang ◽  
Liwei Liu ◽  
Guangwang Su ◽  
Yuanfu Shao
Keyword(s):  
Time Delay ◽  
Food Web ◽  
Numerical Experiments ◽  
Perturbation Technique ◽  
Dynamical Behavior ◽  
Chaotic Oscillation ◽  
Mutual Interference ◽  
Web System ◽  
Distributed Time Delay ◽  
Theoretical Results

In this paper, we present a predator-prey system with mutual interference and distributed time delay and study its dynamical behavior. Based on the existence and universality of mutual interference among species, it is necessary to further study an impulsive food web system. By using stability theory, slight perturbation technique, and comparison theorem, we obtain some theoretical results of the system, such as boundedness and permanence. Moreover, numerical experiments are used to verify the theoretical results and to explore the dynamical behavior of the system, which exhibits rich dynamical behavior such as chaotic oscillation, periodic oscillation, symmetry-breaking bifurcations, chaotic crises, and period bifurcation. Finally, we give some practical guidelines for biological systems based on the theoretical results and numerical experiments of the system.

Vibration Control of a Cantilever Beam with Time Delay State Feedback

2006 ◽  
Vol 61 (12) ◽  
pp. 629-640 ◽  
Author(s):  
Atef F. El-Bassiouny
Keyword(s):  
Time Delay ◽  
Vibration Control ◽  
Cantilever Beam ◽  
State Feedback ◽  
Multiple Scales ◽  
State Feedback Control ◽  
Response Curves ◽  
Flow Equations ◽  
Equivalent Damping ◽  
The Stability

The primary and subharmonic resonance of order one-third of a cantilever beam under state feedback control with a time delay are investigated. Using the method of multiple scales, we obtain two slow flow equations for the amplitude and phase. The first-order approximate solution is derived and the effect of time delay on the resonance is investigated. The concept of an equivalent damping, related to the delay feedback, is proposed and an appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. The fixed points corresponding to the periodic motion of the starting system are determined, and the frequency-response and external excitation-response curves are shown. Bifurcation analysis is conducted in order to examine the stability of the system.

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