Vibration Control by Time Delayed Linear and Non-Linear Acceleration Feedback

2014 ◽  
Vol 592-594 ◽  
pp. 2107-2111 ◽  
Author(s):  
Ranjan Kumar Mitra ◽  
Atul Krishna Banik ◽  
Shymal Chatterjee
Keyword(s):  
Frequency Response ◽  
Duffing Oscillator ◽  
Primary Stability ◽  
Linear Acceleration ◽  
Response Curves ◽  
Gradual Reduction ◽  
Acceleration Feedback ◽  
Good Agreement ◽  
Peak Value ◽  
Appreciable Reduction

The forced Duffing oscillator is investigated by time-delayed linear and nonlinear acceleration feedbacks. The method of Slowly Varying Parameter (SVP) can efficiently develop frequency response curves with stability of solutions. Appreciable reduction in peak value of response and gradual reduction in the skew-ness in frequency response curve is observed with the introduction of gain and delay. For some values of control parameters the entrainment phenomena are also observed. Appropriate choice of gain and delay parameters are made from the primary stability zone of linear stability analysis graph. The results obtained by this method are compared with numerical integration (NI) method and they are in good agreement.

Limit cycle oscillation and multiple entrainment phenomena in a duffing oscillator under time-delayed displacement feedback

2015 ◽  
Vol 23 (17) ◽  
pp. 2742-2756 ◽  
Author(s):  
RK Mitra ◽  
S Chatterjee ◽  
AK Banik
Keyword(s):  
Frequency Response ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Duffing Oscillator ◽  
A Priori ◽  
High Amplitude ◽  
Limit Cycle Oscillation ◽  
Global Dynamics ◽  
Response Curves ◽  
Damped System

The Duffing oscillator under time-delayed displacement feedback is investigated to study the effect of intentional time-delay on the global dynamics of the oscillator. From the free vibration study performed by employing the describing function method it is observed that for the undamped oscillator, an infinite number of limit cycles is present for all possible values of gain and delay. The number of stable and unstable limit cycles in the gain versus delay plane is studied region wise with the help of limit cycle stability lines. Secondly, in a damped system, the number of limit cycles is finite and depends upon the values of gain, delay and damping coefficient from which the maximum number of limit cycles, their frequencies and amplitudes are obtained. When the system is excited by harmonic forcing, these limit cycles exhibit the phenomena of multiple entrainments and their frequency response curves become very complex and most often results in the very high amplitude oscillations. The study of the forced damped oscillator is therefore carried out by applying the method of slowly varying parameter and the frequency response curves for period-1 responses are analyzed. Further, with the a priori knowledge of possible stable and unstable limit cycles obtained by the application of semi-analytical methods, the various instability phenomena due to subharmonic and quasiperiodic responses have also been investigated by numerical simulation using Simulink in the different parametric ranges.

Nonlinear liquid sloshing in a square tank subjected to obliquely horizontal excitation

2012 ◽  
Vol 700 ◽  
pp. 304-328 ◽  
Author(s):  
Takashi Ikeda ◽  
Raouf A. Ibrahim ◽  
Yuji Harata ◽  
Tasuku Kuriyama
Keyword(s):  
Theoretical Analysis ◽  
Frequency Response ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Frequency Range ◽  
Response Curves ◽  
Chaotic Motions ◽  
Nonlinear Responses ◽  
Good Agreement

AbstractNonlinear responses of surface waves in rigid square and nearly square tanks partially filled with liquid subjected to obliquely horizontal, sinusoidal excitation are investigated theoretically and experimentally. Two predominant modes of sloshing are significantly coupled nonlinearly because their natural frequencies are nearly identical resulting in 1:1 internal resonance. Therefore, if only one of these modes is directly excited, the other mode is indirectly excited due to the nonlinear coupling. In the nonlinear theoretical analysis, the modal equations of motion are derived for the two predominant sloshing modes as well as five higher sloshing modes. The linear viscous terms are incorporated in order to consider the damping effect of sloshing. The expressions for the frequency response curves are determined using van der Pol’s method. The influences of the excitation direction and the aspect ratio of the tank cross-section on the frequency response curves are numerically examined. Planar and swirl motions of sloshing, and Hopf bifurcations followed by amplitude modulated motions including chaotic motions, are predicted when the excitation frequency is close to one of the natural frequencies of the two predominant sloshing modes. Lyapunov exponents are calculated and reveal the excitation frequency range over which liquid chaotic motions occur. In addition, bifurcation sets are shown to clarify the influences of the parameters on the change in the structural stability. The theoretically predicted results are in good agreement with the measured data, thus the theoretical analysis was experimentally validated.

scholarly journals On the Nonlinear Dynamics of a Doubly Clamped Microbeam Near Primary Resonance

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Nizar R. Jaber ◽  
Karim M. Masri ◽  
Mohammad I. Younis
Keyword(s):  
Frequency Response ◽  
Primary Resonance ◽  
Single Frequency ◽  
Response Curves ◽  
Shooting Technique ◽  
Softening Behavior ◽  
Dc Bias ◽  
The Stability ◽  
Good Agreement ◽  
Structural Layer

This work aims to investigate theoretically and experimentally various nonlinear dynamic behaviors of a doubly clamped microbeam near its primary resonance. Mainly, we investigate the transition behavior from hardening, mixed, and then softening behavior. We show in a single frequency–response curve, under a constant voltage load, the transition from hardening to softening behavior demonstrating the dominance of the quadratic electrostatic nonlinearity over the cubic geometric nonlinearity of the beam as the motion amplitudes becomes large, which may lead eventually to dynamic pull-in. The microbeam is fabricated using polyimide as a structural layer coated with nickel from top and chromium and gold layers from the bottom. Frequency sweep tests are conducted for different values of direct current (DC) bias revealing hardening, mixed, and softening behavior of the microbeam. A multimode Galerkin model combined with a shooting technique are implemented to generate the frequency–response curves and to analyze the stability of the periodic motions using the Floquet theory. The simulated curves show a good agreement with the experimental data.

Effects of nonlinear interactions of flexural modes on the performance of a beam autoparametric vibration absorber

2019 ◽  
Vol 26 (7-8) ◽  
pp. 459-474
Author(s):  
Saeed Mahmoudkhani ◽  
Hodjat Soleymani Meymand
Keyword(s):  
Frequency Response ◽  
Internal Resonance ◽  
Continuation Method ◽  
Harmonic Balance Method ◽  
Vibration Absorber ◽  
Primary System ◽  
Lumped Mass ◽  
Response Curves ◽  
Internal Resonances ◽  
The One

The performance of the cantilever beam autoparametric vibration absorber with a lumped mass attached at an arbitrary point on the beam span is investigated. The absorber would have a distinct feature that in addition to the two-to-one internal resonance, the one-to-three and one-to-five internal resonances would also occur between flexural modes of the beam by tuning the mass and position of the lumped mass. Special attention is paid on studying the effect of these resonances on increasing the effectiveness and extending the range of excitation amplitudes at which the autoparametric vibration absorber remains effective. The problem is formulated based on the third-order nonlinear Euler–Bernoulli beam theory, where the assumed-mode method is used for deriving the discretized equations of motion. The numerical continuation method is then applied to obtain the frequency response curves and detect the bifurcation points. The harmonic balance method is also employed for detecting the type of internal resonances between flexural modes by inspecting the frequency response curves corresponding to different harmonics of the response. Parametric studies on the performance of the absorber are conducted by varying the position and mass of the lumped mass, while the frequency ratio of the primary system to the first mode of the beam is kept equal to two. Results indicated that the one-to-five internal resonance is especially responsible for the considerable enhancement of the performance.

Study of plate vibrating in fluids having part-through crack at random angles and locations

2021 ◽  
pp. 095440622110127
Author(s):  
Ruqia Ikram ◽  
Asif Israr
Keyword(s):  
Frequency Response ◽  
Multiple Scales ◽  
Peak Amplitude ◽  
Nonlinear Frequency ◽  
Response Curves ◽  
Crack Location ◽  
Cracked Plate ◽  
Nonlinear Frequency Response ◽  
Angle Crack ◽  
Crack Angle

This study presents the vibration characteristics of plate with part-through crack at random angles and locations in fluid. An experimental setup was designed and a series of tests were performed for plates submerged in fluid having cracks at selected angles and locations. However, it was not possible to study these characteristics for all possible crack angles and crack locations throughout the plate dimensions at any fluid level. Therefore, an analytical study is also carried out for plate having horizontal cracks submerged in fluid by adding the influence of crack angle and crack location. The effect of crack angle is incorporated into plate equation by adding bending and twisting moments, and in-plane forces that are applied due to antisymmetric loading, while the influence of crack location is also added in terms of compliance coefficients. Galerkin’s method is applied to get time dependent modal coordinate system. The method of multiple scales is used to find the frequency response and peak amplitude of submerged cracked plate. The analytical model is validated from literature for the horizontally cracked plate submerged in fluid as according to the best of the authors’ knowledge, literature lacks in results for plate with crack at random angle and location in the presence of fluid following validation with experimental results. The combined effect of crack angle, crack location and fluid on the natural frequencies and peak amplitude are investigated in detail. Phenomenon of bending hardening or softening is also observed for different boundary conditions using nonlinear frequency response curves.

Magnification curves of electromagnetic seismographs

1964 ◽  
Vol 54 (5A) ◽  
pp. 1459-1471
Author(s):  
S. K. Chakrabarty ◽  
G. C. Choudhury ◽  
S. N. Roy Choudhury
Keyword(s):  
General Solution ◽  
Frequency Response ◽  
Experimental Method ◽  
Phase Shifts ◽  
Response Curves ◽  
Operating Condition ◽  
Coil Inductance ◽  
The World ◽  
Electromagnetic Seismograph ◽  
Proper Design

Abstract The general solution of the equations connecting the motion of the two coupled components in an electromagnetic seismograph has been obtained in another paper and it shows that the magnification of a seismograph depend on seven instrumental constants. Using these results, equations and curves have been derived in the present paper from which the Magnification as well as Phase shifts in the response of a seismograph and their variations with damping and coil inductance can be easily obtained. Based on these curves a number of magnification curves for different combinations, which are in operation at the different seismological stations of the world, have been derived. Suitable equations and curves have also been obtained which can be used for estimating the absolute Magnification of a Seismograph. An experimental method of obtaining the frequency response curves of seismographs in their operating condition has been described and the results obtained by this method has been given. It has been indicated how the results incorporated in the present paper can be used in the proper design of seismographs required for the different purposes.

Free and Forced Vibrations of the Strongly Nonlinear Cubic-Quintic Duffing Oscillators

2017 ◽  
Vol 72 (1) ◽  
pp. 59-69 ◽  
Author(s):  
M.M. Fatih Karahan ◽  
Mehmet Pakdemirli
Keyword(s):  
Numerical Simulations ◽  
Numerical Solutions ◽  
Multiple Scales ◽  
Approximate Solutions ◽  
Response Curves ◽  
Strongly Nonlinear ◽  
Free And Forced Vibrations ◽  
Approximate Analytical Solutions ◽  
Strongly Nonlinear Oscillators ◽  
Good Agreement

AbstractStrongly nonlinear cubic-quintic Duffing oscillatoris considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions.

scholarly journals Proper motions in the Galactic bulge: Plaut's window

2007 ◽  
Vol 3 (S245) ◽  
pp. 351-354
Author(s):  
Katherine Vieira ◽  
Dana Cassetti-Dinescu ◽  
René A. Méndez ◽  
R. Michael Rich ◽  
Terrence M. Girard ◽  
...  
Keyword(s):  
Proper Motion ◽  
Galactic Rotation ◽  
Red Giants ◽  
Proper Motions ◽  
Motion Study ◽  
Solar Motion ◽  
Two Samples ◽  
Red Clump ◽  
Good Agreement ◽  
Peak Value

AbstractA proper motion study of a field of 20′ × 20′ inside Plaut's low extinction window (l,b)=(0o, −8o), has been completed. Relative proper motions and photographicBVphotometry have been derived for ~ 21,000 stars reaching toV~ 20.5 mag, based on the astrometric reduction of 43 photographic plates, spanning over 21 years of epoch difference. Proper motion errors are typically 1 mas yr−1. Cross-referencing with the 2MASS catalog yielded a sample of ~ 8700 stars, from which predominantly disk and bulge subsamples were selected photometrically from theJHcolor-magnitude diagram. The two samples exhibited different proper-motion distributions, with the disk displaying the expected reflex solar motion. Galactic rotation was also detected for stars between ~2 and ~3 kpc from us. The bulge sample, represented by red giants, has an intrinsic proper motion dispersion of (σl, σb) = (3.39, 2.91)±(0.11, 0.09) mas yr−1, which is in good agreement with previous results. A mean distance of$6.37^{+0.87}_{-0.77}$kpc has been estimated for the bulge sample, based on the observedKmagnitude of the horizontal branch red clump. The metallicity [M/H] distribution was also obtained for a subsample of 60 bulge giants stars, based on calibrated photometric indices. The observed [M/H] shows a peak value at [M/H] ~ −0.1 with an extended metal poor tail and around 30% of the stars with supersolar metallicity. No change in proper motion dispersion was observed as a function of [M/H]. We are currently in the process of obtaining CCDUBV RIphotometry for the entire proper-motion sample of ~ 21,000 stars.

Dynamic Test of Bird Strike on a Flat Plate Made from LY-12 Aluminium

2013 ◽  
Vol 765-767 ◽  
pp. 3158-3161
Author(s):  
Jun Liu ◽  
Zheng Li Zhang
Keyword(s):  
Numerical Simulation ◽  
Dynamic Response ◽  
Dynamic Test ◽  
Time History ◽  
Aircraft Design ◽  
Bird Strike ◽  
Test Results ◽  
Valuable Data ◽  
Good Agreement ◽  
Peak Value

Tests of bird strike have been carried out on plate made from LY-12 Aluminium. The test was down with the projectile impacting the target perpendicularly at velocity of 40m/s, 80m/s, 120m/s respectively. The displacement-time history curves and strain-time history curves of on LY-12 Aluminium plate were measured. The good agreement of the results between two specimens in one group indicated that the results tested in the presnet paper are reliable. The dynamic response of the plate and damage modes of the bird influenced by striking velocity were analyzed. The peak value of the displacement linear enlarged with the increasing of the striking velocity. The test results in the present paper provided valuable data for aircraft design impacted by bird, and also provided abundant test datas for the numerical simulation model applied in bird striking.

Estimation of Transformer Winding Capacitances through Frequency Response Analysis – An Experimental Investigation

2013 ◽  
Vol 14 (6) ◽  
pp. 549-559 ◽  
Author(s):  
Krupa Shah ◽  
K. Ragavan
Keyword(s):  
Frequency Response ◽  
Wide Frequency Range ◽  
Response Analysis ◽  
Voltage Distribution ◽  
Response Data ◽  
Non Invasive ◽  
Transformer Winding ◽  
Invasive Method ◽  
Ladder Network ◽  
Good Agreement

Abstract This article focuses on developing a non-invasive method for determining capacitances using frequency response data. The proposed methodology involves acquiring driving-point impedance of the winding under consideration over wide frequency range. With certain terminal conditions and using the terminal impedance measured at specific frequencies, input and shunt capacitances are determined. For the purpose of estimating series capacitance of the winding, an algorithm is proposed. To demonstrate the capability of the method, initially model coils that have provisions for connecting external capacitances are considered. Then, it is found that the estimated values of capacitances are nearly same as those of connected capacitances. The method is, then, extended to transformer winding, and a capacitive ladder network is constructed. To assess the accuracy of estimation, capacitive voltage distribution is utilized. That is, the voltage distribution in the winding is compared with that of synthesized circuit. A good agreement between those data reveals that the estimated capacitance values are accurate.

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