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 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.

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.

ESO-Based Vibration Control for All-Clamped Plate Using an Electrodynamic Inertial Actuator

2021 ◽  
Author(s):  
Luyao Zhang ◽  
Shengquan Li ◽  
Chaowei Zhu ◽  
Juan Li
Keyword(s):  
Degrees Of Freedom ◽  
Vibration Suppression ◽  
Internal Dynamic ◽  
Clamped Plate ◽  
Tracking Differentiator ◽  
Data Acquisition Card ◽  
Measurement Noises ◽  
The Stability ◽  
External Forces ◽  
Hardware In Loop

This paper proposes a disturbance rejection method with extended state observer (ESO) and a tracking differentiator (TD) to realize vibration suppression of all-clamped plate structure in the presence of lumped disturbance, i.e. internal dynamic uncertainties, unknown external forces and accelerometer measurement noises. First, the structure is modeled as two degrees of freedom system based on vibration characteristics. Second, an ESO is employed to ensure the vibration suppression performance by estimating the lumped disturbances and compensating these disturbances via real-time feedforward mechanism. Meanwhile, a TD is introduced to eliminate the influence of the measurement noises. Moreover, the stability of the closed-loop system is discussed in detail. Finally, the proposed controller is verified on the hardware-in-loop plat-form based on NI PCIe-6343 data acquisition card. Theoretical analysis and experimental results show that the proposed method possesses good vibration suppression performance.

Suppressing the nonlinear vibrations of a compressor blade via a nonlinear saturation controller

2016 ◽  
Vol 24 (8) ◽  
pp. 1488-1504 ◽  
Author(s):  
Ali Kandil ◽  
Hany A El-Gohary
Keyword(s):  
Natural Frequency ◽  
Multiple Scales ◽  
Perturbation Technique ◽  
Time History ◽  
Nonlinear Saturation ◽  
State Equations ◽  
Response Curves ◽  
Rotating Speed ◽  
Main System ◽  
Nonlinear Saturation Controller

A nonlinear saturation controller (NSC) is applied in this work to reduce the oscillations of a rotating blade dynamical system running at unsteady rotating speed. The controller is coupled quadratically to the main system by designing its natural frequency to be one half of the main system natural frequency. This is done to setup an energy bridge between them to make use of saturation phenomenon. That phenomenon is advantageous when the excitation force increases; the whole energy in the main system is channeled to the controller. The two system modes of vibrations are found to be linearly coupled powerfully, so the controller is applied only to the first mode and, consequently, the second mode tracks it. The multiple scales perturbation technique (MSPT) is adopted to derive the steady state equations that describe the modulations of amplitudes and phases of the system before and after control. Then, a stability analysis is achieved via Lyapunov’s indirect method to determine the stable and unstable solutions depending on the real parts of the Jacobian matrix eigenvalues. Time history and different response curves of the controlled system are included for showing the controller effect. Eventually, validation curves and comparison with previously published work are included.

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.

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 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.

Period-1 to Period-2 Motions in a Periodically Forced Nonlinear Spring Pendulum

2019 ◽  
Author(s):  
Albert C. J. Luo ◽  
Yaoguang Yuan
Keyword(s):  
Analytical Solutions ◽  
Perturbation Analysis ◽  
Mapping Method ◽  
Analytical Prediction ◽  
Pendulum System ◽  
Nonlinear Spring ◽  
Period 2 ◽  
Stability And Bifurcations ◽  
The Stability

Abstract In this paper, bifurcation trees of period-1 to period-2 motions in a periodically forced, nonlinear spring pendulum system are predicted analytically through the discrete mapping method. The stability and bifurcations of period-1 to period-2 motions on the bifurcation trees are presented as well. From the analytical prediction, numerical illustrations of period-1 and period-2 motions are completed for comparison of numerical and analytical solutions. The results presented in this paper is totally different from the traditional perturbation analysis.

The Dynamic Simulations of the Ship Towing System in Random Waves

2009 ◽  
Vol 46 (02) ◽  
pp. 107-115
Author(s):  
Ming-Chung Fang ◽  
Jiun-Han Ju
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Time History ◽  
Random Waves ◽  
Dynamic Simulations ◽  
Operation Conditions ◽  
Runge Kutta Method ◽  
Course Stability ◽  
Calm Water ◽  
The Stability

In order to investigate the dynamic stability and safety for a ship towing system operated in waves, the present paper develops a nonlinear mathematical model, including seakeeping and maneuvering characteristics, to simulate dynamic behaviors of the towing system in random waves. In addition to waves, wind is also included in the calculations. The time history simulations of six degrees of freedom motion for both the towing and the towed ships are solved by the fourth-order Runge-Kutta method. Because of the waves, the dynamic properties including the towline tension, ship speeds, headings, and distance between two ships are different from those that occur in calm water. The effects of the towpoint's position, towline length, and towing speed on the ship course stability and towline tension are analyzed with respect to different wave and wind headings. In the present study, the suitable operation conditions for the ship towing system are investigated and can be suggested as a reference for improving the stability and safety of towing operation tasks at sea.

scholarly journals Response Statistics of a Shape Memory Alloy Oscillator with Random Excitation

2021 ◽  
Vol 11 (21) ◽  
pp. 10175
Author(s):  
Rong Guo ◽  
Qi Liu ◽  
Junlin Li ◽  
Yong Xu
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Perturbation Technique ◽  
Time History ◽  
Multiple Scale ◽  
Harmonic Excitation ◽  
Random Excitation ◽  
Random Fluctuation ◽  
Steady State Probability ◽  
Approximate Analytical Solutions

This paper aimed to explore analytically the influences of random excitation on a shape memory alloy (SMA) oscillator. Firstly, on the basis of the deterministic SMA model under a harmonic excitation, we introduce a stochastic SMA model with a narrow-band random excitation. Subsequently, a theoretical analysis for the proposed SMA model was achieved through a multiple-scale method coupled with a perturbation technique. All of the obtained approximate analytical solutions were verified by numerical simulation results, and good agreements were observed. Then, effects of the random excitation and the temperature value on the system responses were investigated in detail. Finally, we found that stochastic switch and bifurcation can be induced by the random fluctuation, which were further illustrated through time history and steady-state probability density function. These results indicate that the random excitation has a significant impact on dynamics of the SMA model. This research provides a certain theoretical basis for the design and vibration control of the SMA oscillator in practical application.

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