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.

Vibration Suppression of a Four-Degrees-of-Freedom Nonlinear Spring Pendulum via Longitudinal and Transverse Absorbers

2011 ◽  
Vol 79 (1) ◽  
Author(s):  
M. Eissa ◽  
M. Kamel ◽  
A. T. El-Sayed
Keyword(s):  
Degrees Of Freedom ◽  
Vibration Suppression ◽  
Perturbation Technique ◽  
Time History ◽  
Multiple Scale ◽  
Threshold Value ◽  
Response Curves ◽  
Pendulum System ◽  
Nonlinear Spring ◽  
The Stability

An investigation into the passive vibration reduction of the nonlinear spring pendulum system, simulating the ship roll motion is presented. This leads to a four-degree-of-freedom (4-DOF) system subjected to multiparametric excitation forces. The two absorbers in the longitudinal and transverse directions are usually designed to control the vibration near the simultaneous subharmonic and internal resonance where system damage is probable. The theoretical results are obtained by applying the multiple scale perturbation technique (MSPT). The stability of the obtained nonlinear solution is studied and solved numerically. The obtained results from the frequency response curves confirmed the numerical results which were obtained using time history. For validity, the numerical solution is compared with the analytical solution. Effectiveness of the absorbers (Ea) are about 13 000 for the first mode (x) and 10 000 for the second mode (ϕ). A threshold value of linear damping coefficient can be used directly for vibration suppression of both vibration modes. Comparison with the available published work is reported.

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.

scholarly journals Positive Position Feedback Controller for Nonlinear Beam Subject to Harmonically Excitation

2019 ◽  
pp. 1-19
Author(s):  
Y. A. Amer ◽  
A. T. EL-Sayed ◽  
A. M. Abdel-Wahab ◽  
H. F. Salman
Keyword(s):  
Time History ◽  
Multiple Scale ◽  
Feedback Controller ◽  
Nonlinear Beam ◽  
Positive Position Feedback ◽  
Simultaneous Resonances ◽  
Position Feedback ◽  
Scale Perturbation ◽  
Response Equation ◽  
Steady State Solutions

In this paper, the vibration reduction of the harmonically excited nonlinear beam is introduced using positive position feedback controller (PPF). The multiple-scale perturbation techniques (MSPT) up is applied to second-order to obtain the analytic results. Numerical simulations are used to compare between time-history and the analytical solution. The frequency response equation (FRE) is studied to illustrate the steady state solutions near the simultaneous resonances. The influences of the different parameters and the system behavior at resonance case are studied to show the optimum conditions of decreasing the vibration. A comparison between the numerical and analytical solutions is presented to appear the validity of the results.

Period Motions and Stability in a Nonlinear Spring Pendulum

2018 ◽  
Author(s):  
Albert C. J. Luo ◽  
Yaoguang Yuan
Keyword(s):  
Fourier Series ◽  
Excitation Frequency ◽  
Analytic Method ◽  
Analytical Prediction ◽  
Discrete Fourier Series ◽  
Periodic Motions ◽  
Harmonic Frequency ◽  
Pendulum System ◽  
Nonlinear Spring ◽  
The Stability

In this paper, period-1 motions varying with excitation frequency in a periodically forced, nonlinear spring pendulum system are predicted by a semi-analytic method. The harmonic frequency-amplitude for periodical motions are analyzed from the finite discrete Fourier series. The stability of the periodical solutions are shown on the bifurcation trees as well. From the analytical prediction, numerical illustrations of periodic motions are given, the comparison of numerical solution and analytical solution are given.

Three Dimensional Fully Localized Waves on Ice-Covered Ocean

2013 ◽  
Author(s):  
Yong Liang ◽  
M.-Reza Alam
Keyword(s):  
Numerical Scheme ◽  
Perturbation Technique ◽  
Three Dimensional ◽  
Multiple Scale ◽  
Governing Equations ◽  
Weakly Nonlinear ◽  
Scale Perturbation ◽  
Speed Of Propagation ◽  
Localized Waves ◽  
Mean Current

We have recently shown [1] that fully-localized three-dimensional wave envelopes (so-called dromions) can exist and propagate on the surface of ice-covered waters. Here we show that the inertia of the ice can play an important role in the size, direction and speed of propagation of these structures. We use multiple-scale perturbation technique to derive governing equations for the weakly nonlinear envelope of monochromatic waves propagating over the ice-covered seas. We show that the governing equations simplify to a coupled set of one equation for the envelope amplitude and one equation for the underlying mean current. This set of nonlinear equations can be further simplified to fall in the category of Davey-Stewartson equations [2]. We then use a numerical scheme initialized with the analytical dromion solution of DSI (i.e. shallow-water and surface-tension dominated regimes of Davey-Stewartson equation) to look for dromion solution of our equations. Dromions can travel over long distances and can transport mass, momentum and energy from the ice-edge deep into the solid ice-cover that can result in the ice cracking/breaking and also in posing dangers to icebreaker ships.

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.

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