Performance Enhancement of an Autoparametric Vibration Absorber Using Multiple Pendulums

2000 ◽  
Author(s):  
Ashwin Vyas ◽  
Anil K. Bajaj ◽  
Arvind Raman
Keyword(s):  
Performance Enhancement ◽  
Excitation Frequency ◽  
Single Mode ◽  
Frequency Interval ◽  
Vibration Absorbers ◽  
Coupled Mode ◽  
Averaged Equations ◽  
Stability And Bifurcations ◽  
The Stability ◽  
Mode Response

Abstract This paper analyzes the dynamics of a resonantly excited single degree-of-freedom linear system coupled to an array of nonlinear autoparametric vibration absorbers (pendulums). The case of a 1:1:…:2 internal resonance between pendulums and the primary oscillator is studied. The method of averaging is used to obtain first-order approximations to the nonlinear response of the system. The stability and bifurcations of the equilibria of the averaged equations are computed. It is shown that the frequency interval of the unstable single-mode response, or the absorber bandwidth, can be enlarged substantially compared to that of a single pendulum absorber by adjusting individually the internal mistunings of the pendulums. Use of multiple pendulums is also shown to engender degenerate bifurcations as the coupled-mode response “switches” from one pendulum to the other with changing external excitation frequency. This results in a significant enhancement of the performance of autoparametric vibration absorbers.

scholarly journals Performance Enhancement in Multicore Fiber Using Trench Assisted Technique

2021 ◽  
Author(s):  
Salma Fatmia ◽  
Manimegalai CT ◽  
Sabitha Gauni ◽  
K. Kalimuthu
Keyword(s):  
Performance Enhancement ◽  
Single Mode ◽  
Design Parameters ◽  
Coupled Mode Theory ◽  
Coupled Mode ◽  
Bending Radius ◽  
Pitch Bending ◽  
Multicore Fiber ◽  
Core Pitch ◽  
Trench Width

Abstract Analysis of crosstalk in multicore fiber using trench assisted technique. To reduce the crosstalk between the cores in the fiber the coupled mode theory and coupled power theory are adopted for crosstalk estimation and considering different design parameters such as core pitch, bending radius and wavelength to optimize the crosstalk performance. The homogeneous fiber which works under single mode operation has been considered. The study of performance by varying the trench width is also analysed. Crosstalk variation in outer cores and center core of the fiber is studied. And the study of variation of crosstalk with 5 different core radius has been done. The numerical simulation results of crosstalk behavior over bending radius, wavelength and trench width is obtained.

Non-Stationary Responses in Externally Excited Two-Degrees-of-Freedom Nonlinear Systems with 1: 2 Internal Resonance

2004 ◽  
Vol 10 (11) ◽  
pp. 1663-1697 ◽  
Author(s):  
Anil K. Bajaj ◽  
Patricia Davies ◽  
Bappaditya Banerjee
Keyword(s):  
Internal Resonance ◽  
Degrees Of Freedom ◽  
Numerical Study ◽  
Excitation Frequency ◽  
Primary Resonance ◽  
Single Mode ◽  
Two Degrees Of Freedom ◽  
Analytical Technique ◽  
Bifurcation Points ◽  
Coupled Mode

The dynamics of two-degrees-of-freedom dynamical systems with weak quadratic nonlinearities is analyzed in the neighborhood of bifurcation points when the excitation frequency varies slowly through the region of primary resonance. The two modes of vibration are in 1: 2 subharmonic internal resonance. The slowly evolving averaged equations are numerically studied for motions initiated in the vicinity of stationary responses, and observations are made about the nature of responses of the system near the transition from single-mode to coupled-mode solutions (pitchfork points), and near jump and Hopf bifurcations in the coupled-mode solutions. An analytical technique based on the dynamic bifurcation theory is developed to explain the numerical observations for passage through the bifurcations. A numerical study is carried out to determine the effects of system parameters on the dynamics near the pitchfork bifurcation points and results are compared with analytical and numerical descriptions of dynamics.

Swing-Up Control of a Three-Link Underactuated Manipulator by High-Frequency Horizontal Excitation

2012 ◽  
Vol 8 (1) ◽  
Author(s):  
Kazuya Endo ◽  
Hiroshi Yabuno
Keyword(s):  
High Frequency ◽  
Multiple Scales ◽  
Equilibrium Points ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Averaged Equations ◽  
Underactuated Manipulator ◽  
High Frequency Excitation ◽  
Pitchfork Bifurcations ◽  
The Stability

In the present paper, we consider a three-link underactuated manipulator, the first joint of which is active and the second and third joints of which exhibit passive motion, on a plane inclined at slight angle from horizontal the plane. We analytically investigate changes in the stability of equilibrium points of the free links connected to the passive joints using high-frequency horizontal excitation of the first link. We derive autonomous averaged equations from the dimensionless equations of motion using the method of multiple scales. We clarify that the two free links can be swung up through pitchfork bifurcations and stabilized at some configurations by producing nontrivial and stable equilibrium points due to the high-frequency excitation. Furthermore, it is experimentally verified that increasing the excitation frequency multiplies stable and nontrivial equilibrium points.

Nonlinear Response of a Clamped Plate to Nonstationary Excitation: Experiments and Theory

1993 ◽  
Author(s):  
Sarah A. McCabe ◽  
Seo I. Chang ◽  
Patricia Davies ◽  
Anil K. Bajaj
Keyword(s):  
Nonlinear Response ◽  
Single Mode ◽  
Theoretical Work ◽  
Sine Wave ◽  
Coupled Mode ◽  
Modal Coupling ◽  
Series Of Experiments ◽  
Initial Objective ◽  
Mode Response ◽  
Sinusoidal Excitation

Abstract The paper contains a description of a series of experiments conducted on a thin rectangular plate. The initial objective of the experiments was to observe behavior predicted by theoretical studies and observed in simulations of the plate response. The theoretical work centered on predicting the behavior of plates having modes with coincident natural frequencies and driven with a constant sinusoidal excitation. Of particular interest was the modal coupling, due to nonlinearities, which give rise to the possibility of a coupled mode response when only a single mode is excited. Experimental constraints, and the sensitivity of the plate in configurations where more than one mode of response is possible, meant that the best experimental excitation of the plate would be a sine wave with a very slowly varying frequency. A PC based signal generator was developed to drive an array of loudspeakers so that particular modes of the plate could be strongly excited, and the frequency of excitation could be varied. To gain an understanding of the behavior of the plate when the excitation is nonstationary, the theoretical analysis of the plate behavior was extended to incorporate sinusoidal excitation where the frequency varied with time. The results of the analysis is a prediction of the response amplitude for slow and relatively fast swept sine wave excitations. In the paper, the qualitative features of the experimental response amplitudes are compared to those predicted by theory.

scholarly journals Correlation and Power Distribution of Intercore Crosstalk Field Components of Polarization-Coupled Weakly Coupled Single-Mode Multicore Fibres

Photonics ◽  
2021 ◽  
Vol 8 (6) ◽  
pp. 191
Author(s):  
José A. P. Morgado ◽  
Adolfo V. T. Cartaxo
Keyword(s):  
Power Distribution ◽  
Communication Systems ◽  
Single Mode ◽  
Coupled Mode ◽  
Weakly Coupled ◽  
Wide Range ◽  
Optical Communication Systems ◽  
The Mean ◽  
Distribution Of Power ◽  
Linear Propagation

The correlation and power distribution of intercore crosstalk (ICXT) field components of weakly coupled multicore fibers (WC-MCFs) are important properties that determine the statistics of the ICXT and ultimately impact the performance of WC-MCF optical communication systems. Using intensive numerical simulation of the coupled mode equations describing ICXT of a single-mode WC-MCF with intracore birefringence and linear propagation, we assess the mean, correlation, and power distribution of the four ICXT field components of unmodulated polarization-coupled homogeneous and quasi-homogeneous WC-MCFs with a single interfering core in a wide range of birefringence conditions and power distribution among the field components at the interfering core input. It is shown that, for homogeneous and quasi-homogeneous WC-MCFs, zero mean uncorrelated ICXT field components with similar power levels are observed for birefringence correlation length and birefringence beat length in the ranges of 0.5m,10m and 0.1m,10m, respectively, regardless of the distribution of power between the four field components at the interfering core input.

An Efficient Galerkin BEM to Compute High Acoustic Eigenfrequencies

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Mario Durán ◽  
Jean-Claude Nédélec ◽  
Sebastián Ossandón
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
High Frequency ◽  
High Accuracy ◽  
Integral Representations ◽  
Stability And Convergence ◽  
Symmetric Matrices ◽  
Frequency Interval ◽  
Numerical Treatment ◽  
The Stability

An efficient numerical method, using integral equations, is developed to calculate precisely the acoustic eigenfrequencies and their associated eigenvectors, located in a given high frequency interval. It is currently known that the real symmetric matrices are well adapted to numerical treatment. However, we show that this is not the case when using integral representations to determine with high accuracy the spectrum of elliptic, and other related operators. Functions are evaluated only in the boundary of the domain, so very fine discretizations may be chosen to obtain high eigenfrequencies. We discuss the stability and convergence of the proposed method. Finally we show some examples.

scholarly journals Effects of Maximal Sodium and Potassium Conductance on the Stability of Hodgkin-Huxley Model

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yue Zhang ◽  
Kuanquan Wang ◽  
Yongfeng Yuan ◽  
Dong Sui ◽  
Henggui Zhang
Keyword(s):  
Experimental Data ◽  
Mathematical Method ◽  
Bifurcation Point ◽  
Potassium Conductance ◽  
Maximal Conductance ◽  
Computing Model ◽  
The World ◽  
Stability And Bifurcations ◽  
The Stability ◽  
Sodium And Potassium

Hodgkin-Huxley (HH) equation is the first cell computing model in the world and pioneered the use of model to study electrophysiological problems. The model consists of four differential equations which are based on the experimental data of ion channels. Maximal conductance is an important characteristic of different channels. In this study, mathematical method is used to investigate the importance of maximal sodium conductanceg-Naand maximal potassium conductanceg-K. Applying stability theory, and takingg-Naandg-Kas variables, we analyze the stability and bifurcations of the model. Bifurcations are found when the variables change, and bifurcation points and boundary are also calculated. There is only one bifurcation point wheng-Nais the variable, while there are two points wheng-Kis variable. The (g-Na,  g-K) plane is partitioned into two regions and the upper bifurcation boundary is similar to a line when bothg-Naandg-Kare variables. Numerical simulations illustrate the validity of the analysis. The results obtained could be helpful in studying relevant diseases caused by maximal conductance anomaly.

Large Amplitude Vibrations of Circular Plate on a Uniform Elastic Foundation

1972 ◽  
Vol 94 (1) ◽  
pp. 43-49 ◽  
Author(s):  
R. Bolton
Keyword(s):  
Circular Plate ◽  
Elastic Foundation ◽  
Normal Modes ◽  
Single Mode ◽  
Linear Mode ◽  
Mode Amplitude ◽  
Plate Vibrations ◽  
Edge Conditions ◽  
Large Amplitude Vibrations ◽  
Mode Response

Herrmann’s equations, the dynamic analogues of the von Karman equations, are solved for a circular plate on a linear elastic foundation by assuming a series solution of the separable form involving unknown time functions. The spatial functions include both regular and modified Bessel functions and are chosen to satisfy the linear mode shape distributions of the plate as well as the usual edge conditions. Total differential equations governing the symmetric plate motions are derived using the Galerkin averaging techniques for a spatially uniform load. By extending the concept of normal modes to nonlinear plate vibrations, comparisons between normal mode response and single mode response, as functions of the first mode amplitude, are shown for different values of the elastic foundation parameter. Results are obtained for plates with simply supported and clamped edges and with both radially moveable and immoveable edges. These results are used to discuss the limitations of single-mode response of circular plates, both with and without an elastic foundation.

scholarly journals Investigating the effect of vibration on the stability of the three-wheeled scooter taxi

2021 ◽  
Vol 39 (4) ◽  
pp. 1117-1122
Author(s):  
S.J. Ojolo ◽  
O.O. Ajayi ◽  
G.A. Asuelinmen
Keyword(s):  
Excitation Frequency ◽  
Vehicle Safety ◽  
Asian Countries ◽  
Wheeled Vehicle ◽  
Safety Margins ◽  
Schematic Layout ◽  
Analysis Design ◽  
The Stability ◽  
The Impact ◽  
Selection Of

The present three wheeled scooter taxi (TWST) that are widespread in Africa and Asian Countries are fuel economical and inexpensive. However, they are unstable due to their schematic layout. This instability places limitation on the usage of the vehicle. Researchers have investigated the rollover and lateral stabilities of this vehicle, including the effect of vibration on the comfort of the riders. However, not much work has been done on the impact of vibration on the stability of the vehicle. These instabilities could be induced by trenches, potholes, uneven and ungraded roads that are prevalent in developing countries. Therefore, this work modelled and analysed the effect of vibration on a TWST using a standard road bump as reference point. The results proved the vehicle to be unstable in the vicinity of excitation frequency of 15.95rad/sec and spring constant of 68,600N/m due to resonance. This would affect safety of life and property. Therefore, it would be appropriate for some of the manufacturers of these vehicles to provide for enough safety margins in the design and selection of springs where the vehicles are rollover and laterally unstable. This will enhance the vehicle safety and receptivity. Keywords: Three wheeled Vehicle, Vibration Modelling and Analysis, Design, Safety of Life and Property

scholarly journals Speaker Localization Based on Audio-Visual Bimodal Fusion

2021 ◽  
Vol 25 (3) ◽  
pp. 375-382
Author(s):  
Ying-Xin Zhu ◽  
Hao-Ran Jin ◽  
◽  
◽  
Keyword(s):  
Microphone Array ◽  
Single Mode ◽  
Frame Rate ◽  
Multimodal Fusion ◽  
Mode Localization ◽  
Localization Method ◽  
Adaboost Algorithm ◽  
Speaker Localization ◽  
The Stability ◽  
Stability And Accuracy

The demand for fluency in human–computer interaction is on an increase globally; thus, the active localization of the speaker by the machine has become a problem worth exploring. Considering that the stability and accuracy of the single-mode localization method are low, while the multi-mode localization method can utilize the redundancy of information to improve accuracy and anti-interference, a speaker localization method based on voice and image multimodal fusion is proposed. First, the voice localization method based on time differences of arrival (TDOA) in a microphone array and the face detection method based on the AdaBoost algorithm are presented herein. Second, a multimodal fusion method based on spatiotemporal fusion of speech and image is proposed, and it uses a coordinate system converter and frame rate tracker. The proposed method was tested by positioning the speaker stand at 15 different points, and each point was tested 50 times. The experimental results demonstrate that there is a high accuracy when the speaker stands in front of the positioning system within a certain range.

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