Pitchfork and Fold/Fold bursting of time delay duffing systems with parametric excitation and external excitation

2021 ◽  
Author(s):  
Yani Chen ◽  
Danjin Zhang ◽  
Bingwen Lin
Keyword(s):  
Time Delay ◽  
Parametric Excitation ◽  
External Excitation

Nonlinear Vibration of Sheet Metal Plates Under Interacting Parametric and External Excitation During Manufacturing

2005 ◽  
Vol 127 (1) ◽  
pp. 36-43 ◽  
Author(s):  
Chung Hwan Kim ◽  
Chong-Won Lee ◽  
N. C. Perkins
Keyword(s):  
Sheet Metal ◽  
Parametric Resonance ◽  
Parametric Excitation ◽  
Synergistic Effects ◽  
Broad Band ◽  
Metal Plate ◽  
Time Dependent ◽  
Single Frequency ◽  
Cubic Nonlinearity ◽  
External Excitation

This study is motivated by the vibrations that plague coating processes used in the manufacturing of coated sheet metal. These vibrations arise from time-dependent tension fluctuations within the sheet metal plate as well as from the eccentricity of the rollers used to transport the plate. The time-dependent tension is observed to be rather broad-band and creates multi-frequency parametric excitation. By contrast, the roller eccentricity is largely single-frequency (synchronized with the roller speed) and creates single-frequency external excitation. The plate and excitation sources are studied herein using a single-degree-of-freedom model with a cubic nonlinearity, subject to combined parametric and external excitation. In our study, we investigate the resonances that arise from the synergistic effects of multi-frequency parametric excitation and single-frequency external excitation. For the simpler case of single-frequency parametric excitation, we observe both sum and difference combination resonances in addition to principal parametric resonance. For the case of multi-frequency parametric excitation, we observe a frequency shift for the parametric resonance that derives from the cubic nonlinearity and external excitation. Moreover, the phase relationships of the external and each parametric excitation source have a significant effect on the resulting response amplitude. We use these analyses to explain the resonance mechanisms observed in experiments conducted on an example sheet metal coating process.

Parametric Resonance of a Self-Excited System Under External Force and Time Delay Influence

2013 ◽  
Author(s):  
Jerzy Warminski ◽  
Anna Warminska
Keyword(s):  
Time Delay ◽  
External Force ◽  
Parametric Resonance ◽  
Parametric Excitation ◽  
Multiple Time ◽  
Frequency Locking ◽  
Scale Method ◽  
Rayleigh Function ◽  
Excited System ◽  
Multiple Time Scale Method

Vibrations of a nonlinear self-excited system driven by parametric excitation are presented in the paper. The considered model with one DOF includes a self-excitation term represented by a nonlinear Rayleigh function and also a periodically varied stiffness coefficient which represents parametric excitation. The influence of the external force or/and time delay, treated as a control signal, is demonstrated. Nonlinear parametric resonance is determined numerically and analytically by the multiple time scale method. The influence of time delay on the resonance zones and the frequency locking phenomenon is analysed.

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 An identification algorithm for feedback active control

2000 ◽  
Vol 22 (4) ◽  
pp. 193-204
Author(s):  
Nguyen Dong Anh
Keyword(s):  
Time Delay ◽  
Control Algorithm ◽  
Opposite Sign ◽  
Control Law ◽  
Identification Algorithm ◽  
Control Force ◽  
Practical Application ◽  
External Excitation ◽  
Time Duration ◽  
Computing Capacity

The aim of the paper is to present a control law for feedback active controlled structures in which a control algorithm is proposed to identify the external excitation with a time delay. The time duration in which the external excitation acts on the structure is devised into subintervals. In each subinterval the external excitation is identified and is then selected with the opposite sign as the control force for the next subinterval. The realization of the identification control algorithm in the practical application mainly depends on the computing capacity of the involved computer. and requires an investigation with respect to its robustness and stabilization.

Nonlinear Vibration of Sheet Metal Plates Under Interacting Parametric and External Excitation During Manufacturing

2003 ◽  
Author(s):  
Chung Hwan Kim ◽  
Chong-Won Lee ◽  
N. C. Perkins
Keyword(s):  
Sheet Metal ◽  
Parametric Resonance ◽  
Parametric Excitation ◽  
Synergistic Effects ◽  
Broad Band ◽  
Metal Plate ◽  
Time Dependent ◽  
Single Frequency ◽  
Cubic Nonlinearity ◽  
External Excitation

This study in motivated by the vibrations that plague coating processes used in the manufacturing of coated sheet metal. These vibrations arise from time-dependent tension fluctuations within the sheet metal plate as well as from the eccentricity of the rollers used to transport the plate. The time-dependent tension is observed to be rather broad-band and creates multi-frequency parametric excitation. By contrast, the roller eccentricity is largely single-frequency (synchronized with the roller speed) and creates single-frequency external excitation. The plate and excitation sources are studied herein using a single-degree-of-freedom model with a cubic nonlinearity, subject to combined parametric and external excitation. In our study, we investigate the resonances that arise from the synergistic effects of multi-frequency parametric excitation and single-frequency external excitation. For the simpler case of single-frequency parametric excitation, we observe both sum and difference combination resonances in addition to principal parametric resonance. For the case of multi-frequency parametric excitation, we observe a frequency shift for the parametric resonance that derives from the cubic nonlinearity and external excitation. Moreover, the phase relationships of the external and each parametric excitation source have a significant effect on the resulting response amplitude. We use these analyses to explain the resonance mechanisms observed in experiments conducted on an example sheet metal coating process.

Stability of a Time-Delayed System With Parametric Excitation

2006 ◽  
Vol 129 (2) ◽  
pp. 125-135 ◽  
Author(s):  
Nitin K. Garg ◽  
Brian P. Mann ◽  
Nam H. Kim ◽  
Mohammad H. Kurdi
Keyword(s):  
Time Delay ◽  
Parametric Excitation ◽  
Mathieu Equation ◽  
Periodic Coefficient ◽  
Single Element ◽  
New Approach ◽  
Delayed System ◽  
Representative Problem ◽  
The Stability ◽  
Time Periodic

This paper investigates two different temporal finite element techniques, a multiple element (h-version) and single element (p-version) method, to analyze the stability of a system with a time-periodic coefficient and a time delay. The representative problem, known as the delayed damped Mathieu equation, is chosen to illustrate the combined effect of a time delay and parametric excitation on stability. A discrete linear map is obtained by approximating the exact solution with a series expansion of orthogonal polynomials constrained at intermittent nodes. Characteristic multipliers of the map are used to determine the unstable parameter domains. Additionally, the described analysis provides a new approach to extract the Floquet transition matrix of time periodic systems without a delay.

STEADY STATE SYMMETRY BREAKING IN PERIODICALLY EXCITED SYSTEMS INVOLVING TIME DELAY BY HARMONIC HOMOTOPY

2013 ◽  
Vol 23 (05) ◽  
pp. 1350091
Author(s):  
A. Y. T. LEUNG ◽  
ZHONGJIN GUO
Keyword(s):  
Steady State ◽  
Time Delay ◽  
Symmetry Breaking ◽  
Moving Load ◽  
Excitation Frequency ◽  
Delayed Feedback Control ◽  
Feedback Gain ◽  
Homotopy Continuation ◽  
External Excitation ◽  
Wide Range

Symmetry breaking is a ubiquitous and important phenomenon arising in a wide range of physical systems. We propose the use of the harmonic balance in combination with homotopy continuation to investigate symmetry breaking occurrence in the periodically excited systems involving time delay. Two numerical examples are given to show the details. When the Hopfield neural network is subject to external excitation, we investigate the relation of the magnitude of excitation versus the amplitude of the bias term and analyze the effect of time delay on the steady state response. The second example concerns the delayed feedback control of a nonlinear beam subject to moving load. The relationship of the position feedback gain, external excitation frequency and time delay versus the amplitudes of steady state responses are studied analytically. The symmetry breaking points are accurately predicted. In addition, the Runge–Kutta numerical simulation results are used to cross-check the efficiency and accuracy.

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