Response of sloping unconfined aquifer to stage changes in adjacent stream. I. Theoretical analysis and derivation of system response functions

The behavior of intrinsic localized modes (ILMs) is investigated for an array with N pendula which are connected with each other by weak, linear springs when the array is subjected to horizontal, sinusoidal excitation. In the theoretical analysis, van der Pol’s method is employed to determine the expressions for the frequency response curves for fundamental harmonic oscillations. In the numerical calculations, the frequency response curves are presented for N = 2 and 3 and compared with the results of the numerical simulations. Patterns of oscillations are classified according to the stable steady-state solutions of the response curves, and the patterns in which ILMs appear are discussed in detail. The influence of the connecting springs of the pendula on the appearance of ILMs is examined. Increasing the values of the connecting spring constants may affect the excitation frequency range of ILMs and cause Hopf bifurcation to occur, followed by amplitude modulated motions (AMMs) including chaotic vibrations. The influence of the imperfections of the pendula on the system response is also investigated. Bifurcation sets are calculated to examine the influence of the system parameters on the excitation frequency range of ILMs and determine the threshold value for the connecting spring constant after which ILMs do not appear. Experiments were conducted for N = 2, and the data were compared with the theoretical results in order to confirm the validity of the theoretical analysis.

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Correlation of Theoretical Analysis With Experimental Data on The Performance of Charring Ablators

Journal of Heat Transfer ◽

10.1115/1.3450457 ◽

1976 ◽

Vol 98 (1) ◽

pp. 139-143 ◽

Cited By ~ 3

Author(s):

K. Mastanaiah

Keyword(s):

Experimental Data ◽

Thermal Conductivity ◽

Heat Flux ◽

Theoretical Analysis ◽

Experimental System ◽

Wall Heat Flux ◽

System Response ◽

Exponential Dependence ◽

Cold Wall ◽

Static Test

Experimental data are obtained for surface recession, char depth, and temperatures in silica phenolic and carbon phenolic ablators from static test conducted on rocket nozzles. In an attempt to correlate the theoretical analysis with the experimental observations, it is found that the effective thermal conductivity of char is strongly dependent on the wall heat flux. An hypothesis is postulated that the char conductivity can best be correlated by cold wall heat flux treated as a generalized variable that includes the effects of other factors like temperature and chemical composition of the char. Exponential dependence of char conductivity on the cold wall heat flux is observed for both the ablators, and has offered excellent comparison between the theoretical and the experimental system response.

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Nonlinear Camera Response Functions and Image Deblurring: Theoretical Analysis and Practice

IEEE Transactions on Pattern Analysis and Machine Intelligence ◽

10.1109/tpami.2013.40 ◽

2013 ◽

Vol 35 (10) ◽

pp. 2498-2512 ◽

Cited By ~ 40

Author(s):

Yu-Wing Tai ◽

Xiaogang Chen ◽

Sunyeong Kim ◽

Seon Joo Kim ◽

Feng Li ◽

...

Keyword(s):

Theoretical Analysis ◽

Image Deblurring ◽

Response Functions

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A Theoretical Analysis of Camera Response Functions in Image Deblurring

Computer Vision – ECCV 2012 - Lecture Notes in Computer Science ◽

10.1007/978-3-642-33786-4_25 ◽

2012 ◽

pp. 333-346 ◽

Cited By ~ 7

Author(s):

Xiaogang Chen ◽

Feng Li ◽

Jie Yang ◽

Jingyi Yu

Keyword(s):

Theoretical Analysis ◽

Image Deblurring ◽

Response Functions

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Fast Calculation of the Statistics of the Forced Response of Mistuned Bladed Disk Assemblies With Friction Contacts

Volume 4: Turbo Expo 2002, Parts A and B ◽

10.1115/gt2002-30427 ◽

2002 ◽

Cited By ~ 3

Author(s):

Walter Sextro ◽

Lars Panning ◽

Florian Go¨tting ◽

Karl Popp

Keyword(s):

Monte Carlo ◽

Monte Carlo Simulations ◽

Frequency Response ◽

Approximate Method ◽

Natural Frequencies ◽

Computation Time ◽

System Response ◽

Response Functions ◽

Frequency Response Functions ◽

Bladed Disk

In turbomachinery one major problem is still the calculation and the optimization of the spatial vibrations of mistuned bladed disk assemblies with friction contacts. Friction contacts are widely used to reduce dynamic stresses in turbine blades. Due to dry friction and the relative motion of the contact planes energy is dissipated. This effect results in a reduction of blade vibration amplitudes. In the case of a tuned bladed disk cyclic boundary conditions can be used for the calculation of the dynamic response. For a mistuned bladed disk the complete system has to be modeled and simulated. To reduce the computation time the so-called substructure method is applied. This method is based on the modal description of each substructure, especially disk and blades, combined with a reduction of the degrees of freedom, to describe the dynamics of each component. The spatial dynamical behavior of each component is considered and described by the mode shapes, natural frequencies and modal damping ratios. Using the Harmonic Balance Method the nonlinear friction forces can be linearized. From here it is possible to calculate the frequency response functions of a mistuned bladed disk assembly with friction contacts. In many cases Monte-Carlo simulations are used to find regions, where the system response is sensitive to parameter uncertainties like the natural frequencies of the blades. These simulations require a large computation time. Therefore, an approximate method is developed to calculate the envelopes of the frequency response functions for statistically varying natural frequencies of the blades. This method is based on a sensitivity analysis and the Weibull-distribution of the vibration amplitudes. From here, a measure for the strength of localization for mistuned cyclic systems is derived. Regions, where localization can occur with a high probability, can be calculated by this method. The mean value and the standard deviation of the vibration amplitudes are calculated by simulation and by the approximate method. The comparisons between the approximate method and the Monte-Carlo simulations show a good agreement. Therefore, applying this method leads to remarkable reduction of computation time and gives a quick insight into the system behavior. The approximate method can also be applied to systems, that include the elasticity of the disk and/or the coupling by shrouds or other friction devices.

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Model Validation of Functional Responses Across Experimental Regions Using Functional Regression Extensions to the CORA Objective Rating System

Journal of Verification Validation and Uncertainty Quantification ◽

10.1115/1.4039303 ◽

2017 ◽

Vol 2 (4) ◽

Author(s):

Scott M. Storm ◽

Raymond R. Hill ◽

Joseph J. Pignatiello ◽

G. Geoffrey Vining ◽

Edward D. White

Keyword(s):

Functional Data ◽

Rating System ◽

System Response ◽

Functional Regression ◽

Response Functions ◽

Weighted Linear Combination ◽

Functional Responses ◽

Parameter Configuration ◽

Objective Rating ◽

The Individual

As we continue to model more complex systems, the validation of dynamical responses has come to the forefront of modeling and simulation. One form of dynamic response is when the output is a function of time. The proper evaluation of functional data over an array of desired input parameters is critical to achieving a robust validation assessment of a simulation model. We extend the correlation analysis (CORA) objective rating system to validate functional data across experimental regions. Functional regression analysis is used to generate surrogate estimations of the system response functions at points within the region where experimental observations are absent. These CORA scores provide a measure of disagreement at each desired parameter configuration. An overall score for model validity is achieved using a weighted linear combination of the individual CORA scores. Finally, an improved CORA size scoring metric is introduced.

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A Theoretical Analysis of Transient Sound Radiation From a Clamped Circular Plate

Journal of Applied Mechanics ◽

10.1115/1.3167595 ◽

1984 ◽

Vol 51 (1) ◽

pp. 41-47 ◽

Cited By ~ 7

Author(s):

A. Akay ◽

M. Tokunaga ◽

M. Latcha

Keyword(s):

Theoretical Analysis ◽

Circular Plate ◽

Impulse Response ◽

Sound Radiation ◽

Free Vibrations ◽

Mode Shapes ◽

Impulse Response Functions ◽

Response Functions ◽

Surface Integral ◽

Pressure Impulse

A theoretical analysis of transient sound radiation from a clamped circular plate is given using a pressure impulse response method. The vibration response of the plate to a transient point force is obtained. The modal pressure impulse response functions for the plate are derived from the Rayleigh surface integral and numerically convoluted with the modal acceleration response of the plate. The impulse response functions are closely related to the mode shapes and the geometry of the problem. They relate the spatial domain to the temporal domain of the pressure waves. The pressure impulse response waveforms are given for a number of plate modes and the changes in the waveforms with distance from the plate are shown. Sound radiation due to forced and free vibrations of the plate are discussed.

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Experience-Dependent Color Constancy in Guppies (Poecilia reticulata)

Neural Plasticity ◽

10.1155/np.2002.205 ◽

2002 ◽

Vol 9 (3) ◽

pp. 205-216 ◽

Cited By ~ 4

Author(s):

I. E. Intskirveli ◽

M. O. Roinishvili ◽

A. R. Kezeli

Keyword(s):

Poecilia Reticulata ◽

Visual Experience ◽

Color Constancy ◽

System Response ◽

Control Group ◽

Artificial Light ◽

Response Functions ◽

Spectral Content ◽

Lighting Conditions ◽

Full Development

We investigated the ability to recognize the color of surfaces in fish (Poecilia reticulata), bred from birth in conditions of artificial light with constant spectral content. The capacity for color constancy significantly deteriorated when compared that to the control group. Further alteration of lighting conditions and transfer into natural daylight conditions restored the suppressed function to its normal level. We suggest that the color constancy function belongs in the visual system-response functions, the full development of which requires the accumulation of individual visual experience.

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Singular Loss of Stability Due to Hysteretic Capillary Forces in Atomic Force Microscopy

Volume 4: 12th International Conference on Advanced Vehicle and Tire Technologies; 4th International Conference on Micro- and Nanosystems ◽

10.1115/detc2010-28686 ◽

2010 ◽

Author(s):

Michael Katzenbach ◽

Harry Dankowicz

Keyword(s):

Atomic Force Microscopy ◽

Theoretical Analysis ◽

Deterministic Model ◽

Fluid Layer ◽

Mapping Technique ◽

System Response ◽

Force Microscopy ◽

Atomic Force ◽

Critical Equilibrium ◽

Linearized Stability

This paper considers discontinuity-induced bifurcations due to the onset and termination of hysteretic, capillary tip-sample interaction forces in a single-mechanical-mode model of intermittent-contact atomic-force microscopy. The theoretical analysis generalizes earlier results for a piecewise-linear hybrid dynamical system to establish the singular termination of branches of steady-state oscillations of the AFM cantilever at critical equilibrium separations corresponding to the grazing contact of the cantilever tip with a fluid layer deposited on the sample. It is shown that this termination is preceded by rapid changes in linearized stability characteristics with one characteristic multiplier going to plus or minus infinity in the deterministic model. The paper describes the application of a discontinuity-mapping technique that allows for unfolding the system response in the vicinity of the grazing condition and the critical equilibrium separation. Numerical simulations and results of parameter continuation are shown to closely agree with the predictions of the theoretical analysis.

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