A Transfer-Function Formulation For Nonuniformly Distributed Parameter Systems

This paper studies a transfer-function formulation for general one-dimensional, nonuniformly distributed systems, subject to arbitrary boundary conditions and external disturbances. In the development, the governing equations of the nonuniform system are cast into a state-space form in the Laplace transform domain. The system response and distributed transfer functions are derived in term of the fundamental matrix of the state-space equation. Two approximate methods, the step-function approximation and truncated Taylor series, are proposed to evaluate the fundamental matrix. With the transfer-function formulation, various dynamics and control problems for the nonuniformly distributed system can be conveniently addressed. The transfer-function analysis also is applied to constrained/combined nonuniformly distibuted systems. The method developed is illustrated on two nonuniform beams.

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Transfer Function Analysis of Non-Uniformly Distributed Parameter Systems

14th Biennial Conference on Mechanical Vibration and Noise: Vibration and Control of Mechanical Systems ◽

10.1115/detc1993-0223 ◽

1993 ◽

Author(s):

Bingen Yang ◽

Houfei Fang

Keyword(s):

Distributed Systems ◽

Transfer Function ◽

State Space ◽

Fundamental Matrix ◽

Function Analysis ◽

Distributed Parameter Systems ◽

System Response ◽

Distributed Parameter ◽

Transfer Function Analysis ◽

Function Formulation

Abstract This paper studies a transfer function formulation for general one-dimensional, non-uniformly distributed systems subject to arbitrary boundary conditions and external disturbances. The purpose is to provide an useful alternative for modeling and analysis of distributed parameter systems. In the development, the system equations of the non-uniform system are cast into a state space form in the Laplace transform domain. The system response and distributed transfer functions are derived in term of the fundamental matrix of the state space equation. Two approximate methods for evaluating the fundamental matrix are proposed. With the transfer function formulation, various dynamics and control problems for the non-uniformly distributed system can be conveniently addressed. The transfer function analysis is also applied to constrained/combined non-uniformly distributed systems.

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Transfer function analysis of autonomic regulation. I. Canine atrial rate response

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.1989.256.1.h142 ◽

1989 ◽

Vol 256 (1) ◽

pp. H142-H152 ◽

Cited By ~ 110

Author(s):

R. D. Berger ◽

J. P. Saul ◽

R. J. Cohen

Keyword(s):

Transfer Function ◽

Transfer Functions ◽

Function Analysis ◽

Cardiac Pacemaker ◽

Corner Frequency ◽

Pass Filter ◽

Low Pass Filter ◽

Atrial Rate ◽

Transfer Function Analysis ◽

Functional Components

We present a useful technique for analyzing the various functional components that comprise the cardiovascular control network. Our approach entails the imposition of a signal with broad frequency content as an input excitation and the computation of a system transfer function using spectral estimation techniques. In this paper, we outline the analytical methods involved and demonstrate the utility of our approach in studying the dynamic behavior of the canine cardiac pacemaker. In particular, we applied frequency-modulated pulse trains to either the right vagus or the cardiac sympathetic nerve and computed transfer functions between nerve stimulation rate and the resulting atrial rate. We found that the sinoatrial node (and associated automatic tissue) responds as a low-pass filter to fluctuations in either sympathetic or parasympathetic tone. For sympathetic fluctuations, however, the filter has a much lower corner frequency than for vagal fluctuations and is coupled with a roughly 1.7-s pure delay. We further found that the filter characteristics, including the location of the corner frequency and rate of roll-off, depend significantly on the mean level of sympathetic or vagal tone imposed.

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Transfer function analysis of the circulation: unique insights into cardiovascular regulation

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.1991.261.4.h1231 ◽

1991 ◽

Vol 261 (4) ◽

pp. H1231-H1245 ◽

Cited By ~ 145

Author(s):

J. P. Saul ◽

R. D. Berger ◽

P. Albrecht ◽

S. P. Stein ◽

M. H. Chen ◽

...

Keyword(s):

Transfer Function ◽

Arterial Pressure ◽

Transfer Functions ◽

Function Analysis ◽

Pressure Fluctuations ◽

Rate Of Change ◽

Phase Delay ◽

Sinus Arrhythmia ◽

Mechanical Effects ◽

Transfer Function Analysis

We have demonstrated previously that transfer function analysis can be used to precisely characterize the respiratory sinus arrhythmia (RSA) in normal humans. To further investigate the role of the autonomic nervous system in RSA and to understand the complex links between respiratory activity and arterial pressure, we determined the transfer functions between respiration, heart rate (HR), and phasic, systolic, diastolic, and pulse arterial pressures in 14 healthy subjects during 6-min periods in which the respiratory rate was controlled in a predetermined but erratic fashion. Pharmacological autonomic blockade with atropine, propranolol, and both, in combination with changes in posture, was used to characterize the sympathetic and vagal contributions to these relationships, as well as to dissect the direct mechanical links between respiration and arterial pressure from the effects of the RSA on arterial pressure. We found that 1) the pure sympathetic (standing + atropine) HR response is characterized by markedly reduced magnitude at frequencies greater than 0.1 Hz and a phase delay, whereas pure vagal (supine + propranolol) modulation of HR is characterized by higher magnitude at all frequencies and no phase delay; 2) both the mechanical links between respiration and arterial pressure and the RSA contribute significantly to the effects of respiration on arterial pressure; 3) the RSA contribution to arterial pressure fluctuations is significant for vagal but not for sympathetic modulation of HR; 4) the mechanical effects of respiration on arterial pressure are related to the negative rate of change of instantaneous lung volume; 5) the mechanical effects have a higher magnitude during systole than during diastole; and 6) the mechanical effects are larger in teh standing than the supine position. Most of these findings can be explained by a simple model of circulatory control based on previously published experimental transfer functions from our laboratory.

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An improved statistical methodology to estimate and analyze impedances and transfer functions

Journal of Applied Physiology ◽

10.1152/jappl.1997.83.6.2146 ◽

1997 ◽

Vol 83 (6) ◽

pp. 2146-2157 ◽

Cited By ~ 2

Author(s):

Douglas Curran-Everett ◽

Yiming Zhang ◽

M. Douglas Jones ◽

Richard H. Jones

Keyword(s):

Time Series ◽

Transfer Function ◽

Fourier Transforms ◽

Transfer Functions ◽

Function Analysis ◽

Statistical Methodology ◽

Test Statistic ◽

Discrete Fourier Transforms ◽

Repeated Observations ◽

Transfer Function Analysis

Curran-Everett, Douglas, Yiming Zhang, M. Douglas Jones, Jr., and Richard H. Jones. An improved statistical methodology to estimate and analyze impedances and transfer functions. J. Appl. Physiol. 83: 2146–2157, 1997.—Estimating the mathematical relationship between pulsatile time series (e.g., pressure and flow) is an effective technique for studying dynamic systems. The frequency-domain relationship between time series, often calculated as an impedance (pressure/flow), is known more generally as a frequency-response or transfer function (output/input). Current statistical methods for transfer function analysis 1) assume erroneously that repeated observations on a subject are independent, 2) have limited statistical value and power, or 3) are restricted to use in single subjects rather than in an entire sample. This paper develops a regression model for transfer function analysis that corrects each of these deficiencies. Spectral densities of the input and output time series and the cross-spectral density between them are first estimated from discrete Fourier transforms and then used to obtain regression estimates of the transfer function. Statistical comparisons of the transfer function estimates use a test statistic that is distributed as χ2. Confidence intervals for amplitude and phase can also be calculated. By correctly modeling repeated observations on each subject, this improved statistical approach to transfer function estimation and analysis permits the simultaneous analysis of data from all subjects in a sample, improves the power of the transfer function model, and has broad relevance to the study of dynamic physiological systems.

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A general transfer function representation for a class of hyperbolic distributed parameter systems

International Journal of Applied Mathematics and Computer Science ◽

10.2478/amcs-2013-0022 ◽

2013 ◽

Vol 23 (2) ◽

pp. 291-307 ◽

Cited By ~ 12

Author(s):

Krzysztof Bartecki

Keyword(s):

Transfer Function ◽

Transfer Functions ◽

Function Analysis ◽

Semigroup Theory ◽

Distributed Parameter Systems ◽

Hyperbolic Partial Differential Equations ◽

Distributed Parameter ◽

Function Representation ◽

Tube Heat Exchanger ◽

Transfer Function Analysis

Results of transfer function analysis for a class of distributed parameter systems described by dissipative hyperbolic partial differential equations defined on a one-dimensional spatial domain are presented. For the case of two boundary inputs, the closed-form expressions for the individual elements of the 2×2 transfer function matrix are derived both in the exponential and in the hyperbolic form, based on the decoupled canonical representation of the system. Some important properties of the transfer functions considered are pointed out based on the existing results of semigroup theory. The influence of the location of the boundary inputs on the transfer function representation is demonstrated. The pole-zero as well as frequency response analyses are also performed. The discussion is illustrated with a practical example of a shell and tube heat exchanger operating in parallel- and countercurrent-flow modes.

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Distributed Transfer Function Analysis of Ring-Stiffened Cylindrical Shells

Volume 3C: 15th Biennial Conference on Mechanical Vibration and Noise — Vibration Control, Analysis, and Identification ◽

10.1115/detc1995-0652 ◽

1995 ◽

Author(s):

J. Zhou ◽

B. Yang

Keyword(s):

Transfer Function ◽

Transfer Functions ◽

Function Analysis ◽

Cylindrical Shells ◽

Middle Surface ◽

Mode Shapes ◽

Structural Components ◽

Stiffened Shells ◽

Transfer Function Analysis ◽

Stiffened Cylindrical Shells

Abstract A new analytical and numerical method is presented for modeling and analysis of cylindrical shells stiffened by circumferential rings. This method treats the shell and ring stiffeners as individual structural components, and considers the ring eccentricity with respect to the shell middle surface. Through use of the distributed transfer functions of the structural components, various static and dynamic problems of stiffened shells are systematically formulated. With this transfer function formulation, the static and dynamic response, natural frequencies and mode shapes, and buckling loads of general stiffened cylindrical shells under arbitrary external excitations and boundary conditions can be determined in exact and closed-form. The proposed method is illustrated on a Donnell-Mushtari shell, and compared with finite element method and two other modeling techniques.

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Spatial Unmasking Effect on Speech Reception Threshold in the Median Plane

Applied Sciences ◽

10.3390/app10155257 ◽

2020 ◽

Vol 10 (15) ◽

pp. 5257

Author(s):

Nathan Berwick ◽

Hyunkook Lee

Keyword(s):

Transfer Function ◽

Input Signal ◽

Function Analysis ◽

Median Plane ◽

Speech Reception ◽

Transfer Function Analysis ◽

Spatial Unmasking ◽

Head Related Transfer Function ◽

Speech Reception Thresholds ◽

Energy Weighting

This study examined whether the spatial unmasking effect operates on speech reception thresholds (SRTs) in the median plane. SRTs were measured using an adaptive staircase procedure, with target speech sentences and speech-shaped noise maskers presented via loudspeakers at −30°, 0°, 30°, 60° and 90°. Results indicated a significant median plane spatial unmasking effect, with the largest SRT gain obtained for the −30° elevation of the masker. Head-related transfer function analysis suggests that the result is associated with the energy weighting of the ear-input signal of the masker at upper-mid frequencies relative to the maskee.

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