An Experimental Study of the Forced Response of Pre- and Post-Critical Plates

1995 ◽  
Author(s):  
Kevin D. Murphy ◽  
Lawrence N. Virgin ◽  
Stephen A. Rizzi
Keyword(s):  
Experimental Study ◽  
Time Series ◽  
Lyapunov Exponent ◽  
Small Amplitude ◽  
Narrow Band ◽  
Power Spectra ◽  
Forced Response ◽  
Acoustic Excitation ◽  
Rectangular Plates ◽  
Auto Correlation

Abstract Experimental results are presented which characterize the dynamic response of homogeneous, fully clamped, rectangular plates to narrow band acoustic excitation and uniform thermal loads. Using time series, pseudo-phase projections, power spectra and auto-correlation functions, small amplitude vibrations are considered about both the pre- and post-critical states. These techniques are then employed to investigate the snap-through response. The results for snap-through suggest that the motion is temporally complex and a Lyapunov exponent calculation confirms that the motion is chaotic. Finally, a snap-through boundary is mapped in the (ω, SPL) parameter space separating the regions of snap-through and no snap-through.

Identification of Nonlinear and Chaotic Behavior in Model-Scale Liquefied Natural Gas (LNG) Carrier Experimental Data

2005 ◽  
Author(s):  
Leigh S. McCue ◽  
Armin W. Troesch
Keyword(s):  
Experimental Data ◽  
Experimental Study ◽  
Time Series ◽  
Lyapunov Exponent ◽  
Chaotic Behavior ◽  
Surrogate Data ◽  
Liquefied Natural Gas ◽  
Nonlinear Time Series Analysis ◽  
Beam Seas ◽  
Fluid Sloshing

This paper presents the results of an experimental study simulating the behavior of LNG carriers with partially filled tanks exposed to beam seas. Details of the experimental model and method of data collection are presented. Additionally, surrogate data testing is employed to demonstrate nonlinearity in vessel roll time series. Lastly, Lyapunov exponent calculations are performed to detect chaotic behavior resulting from nonlinear vessel motions coupled with the dynamics of fluid sloshing in on-board tanks. The nonlinear time series analysis programs contained in the TISEAN package [1] are used extensively throughout this work.

Dynamics of SC-CNN Based Variant of MLC Circuit: An Experimental Study

2014 ◽  
Vol 24 (02) ◽  
pp. 1430008 ◽  
Author(s):  
P. S. Swathy ◽  
K. Thamilmaran
Keyword(s):  
Neural Network ◽  
Experimental Study ◽  
Time Series ◽  
Power Spectra ◽  
Cellular Neural Network ◽  
Phase Portraits ◽  
Onset Of Chaos ◽  
Experimental Time Series ◽  
The Stability ◽  
Good Agreement

In this paper, a State Controlled Cellular Neural Network (SC-CNN) based variant of Murali–Lakshmanan–Chua (MLCV) circuit is presented. The proposed system is modeled by using a suitable connection of two simple state controlled generalized CNN cells, while the stability of the circuit is studied by determining the eigenvalues of the stability matrices, the dynamics as well as onset of chaos, torus and bifurcation have been investigated through laboratory hardware experiments and numerical analysis of the generalized SC-CNN equations. The experimental results such as phase portraits, Poincaré map and power spectra are in good agreement with those of numerical computations. We further validate our findings with data obtained from both experimental time series observations and numerical simulations and discuss "0-1 test" for distinguishing quasiperiodicity and chaoticity, which successfully detects the transition. The results obtained are quite satisfactory and significant.

Model of multicomponent narrow-band periodical non-stationary random signal

2020 ◽  
Vol 2020 (48) ◽  
pp. 17-24
Author(s):  
I.M. Javorskyj ◽  
◽  
R.M. Yuzefovych ◽  
P.R. Kurapov ◽  
◽  
...  
Keyword(s):  
Time Series ◽  
Real Time ◽  
Hilbert Transform ◽  
Spectral Properties ◽  
Narrow Band ◽  
Analytic Signal ◽  
Random Signal ◽  
Hilbert Transformation ◽  
The Hilbert Transform

The correlation and spectral properties of a multicomponent narrowband periodical non-stationary random signal (PNRS) and its Hilbert transformation are considered. It is shown that multicomponent narrowband PNRS differ from the monocomponent signal. This difference is caused by correlation of the quadratures for the different carrier harmonics. Such features of the analytic signal must be taken into account when we use the Hilbert transform for the analysis of real time series.

EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Time Series Data ◽  
Logistic Map ◽  
Model Identification ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

The Lyapunov Exponent Variance of an Electronic Manufacturing Enterprise’s Daily Qualified Rate Time Series by Improved Small Data Sets Approach

2012 ◽  
Vol 197 ◽  
pp. 271-277
Author(s):  
Zhu Ping Gong
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Chaotic Time Series ◽  
Quality System ◽  
Quality Level ◽  
Largest Lyapunov Exponent ◽  
Small Data ◽  
Data Set ◽  
Electronic Manufacturing ◽  
Small Data Set

Small data set approach is used for the estimation of Largest Lyapunov Exponent (LLE). Primarily, the mean period drawback of Small data set was corrected. On this base, the LLEs of daily qualified rate time series of HZ, an electronic manufacturing enterprise, were estimated and all positive LLEs were taken which indicate that this time series is a chaotic time series and the corresponding produce process is a chaotic process. The variance of the LLEs revealed the struggle between the divergence nature of quality system and quality control effort. LLEs showed sharp increase in getting worse quality level coincide with the company shutdown. HZ’s daily qualified rate, a chaotic time series, shows us the predictable nature of quality system in a short-run.

Study of Rehabilitation of Injured Knee Joint Applying Chaotic Theory in Human Body Motion

2007 ◽  
Vol 342-343 ◽  
pp. 581-584
Author(s):  
Byung Young Moon ◽  
Kwon Son ◽  
Jung Hong Park
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Angular Displacement ◽  
Three Dimensional ◽  
Gait Pattern ◽  
Body Motion ◽  
Largest Lyapunov Exponent ◽  
Chaos Analysis ◽  
Nonlinear Technique ◽  
Injured Knee

Gait analysis is essential to identify accurate cause and knee condition from patients who display abnormal walking. Traditional linear tools can, however, mask the true structure of motor variability, since biomechanical data from a few strides during the gait have limitation to understanding the system. Therefore, it is necessary to propose a more precise dynamic method. The chaos analysis, a nonlinear technique, focuses on understanding how variations in the gait pattern change over time. Healthy eight subjects walked on a treadmill for 100 seconds at 60 Hz. Three dimensional walking kinematic data were obtained using two cameras and KWON3D motion analyzer. The largest Lyapunov exponent from the measured knee angular displacement time series was calculated to quantify local stability. This study quantified the variability present in time series generated from gait parameter via chaos analysis. Gait pattern is found to be chaotic. The proposed Lyapunov exponent can be used in rehabilitation and diagnosis of recoverable patients.

scholarly journals Determination of the complex frequencies for the normal modes below 1mHz after the 2010 Maule and 2011 Tohoku earthquakes

2014 ◽  
Vol 56 (5) ◽  
Author(s):  
Hao Ding ◽  
Wen-Bin Shen
Keyword(s):  
Time Series ◽  
Normal Modes ◽  
Power Spectra ◽  
Tohoku Earthquake ◽  
Superconducting Gravimeter ◽  
Width Ratio ◽  
Maule Earthquake ◽  
Attenuation Models ◽  
First Time

<p>Based upon SG (superconducting gravimeter) records, the autoregressive method proposed by Chao and Gilbert [1980] is used to determine the frequencies of the singlets of seven spheroidal modes (<sub>0</sub>S<sub>2</sub>, <sub>2</sub>S<sub>1</sub>, <sub>0</sub>S<sub>3</sub>, <sub>0</sub>S<sub>4</sub>, <sub>1</sub>S<sub>2</sub>, <sub>0</sub>S<sub>0</sub>, and <sub>3</sub>S<sub>1</sub>) and the degenerate frequencies of three toroidal modes (<sub>0</sub>T<sub>2</sub>, <sub>0</sub>T<sub>3</sub>, and <sub>0</sub>T<sub>4</sub>) below 1 mHz after two recent huge earthquakes, the 2010 Mw8.8 Maule earthquake and the 2011 Mw9.1 Tohoku earthquake. The corresponding quality factor <em>Q</em>s are also determined for those modes, of which the <em>Q</em>s of the five singlets of <sub>1</sub>S<sub>2</sub> and the five singlets (<em>m</em>=0, <em>m</em>=±2, and <em>m</em>=±3) of <sub>0</sub>S<sub>4</sub> are estimated for the first time using the SG observations. The singlet <em>m</em>=0 of <sub>3</sub>S<sub>1</sub> is clearly observed from the power spectra of the SG time series without using other special spectral analysis methods or special time series from pole station records. In addition, the splitting width ratio <em>R</em> of <sub>3</sub>S<sub>1</sub> is 0.99, and consequently we conclude that <sub>3</sub>S<sub>1</sub> is normally split. The frequencies and <em>Q</em>s of the modes below 1mHz may contribute to refining the 3D density and attenuation models of the Earth.</p>

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