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

2013 ◽  
Vol 23 (2) ◽  
pp. 291-307 ◽  
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.

Transfer Function Analysis of Non-Uniformly Distributed Parameter Systems

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.

Transfer Functions of One-Dimensional Distributed Parameter Systems by Wave Approach

2006 ◽  
Vol 129 (2) ◽  
pp. 193-201 ◽  
Author(s):  
B. Kang
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Wave Reflection ◽  
Transfer Functions ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Complex Frequency ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Analysis Technique

An alternative analysis technique, which does not require eigensolutions as a priori, for the dynamic response solutions, in terms of the transfer function, of one-dimensional distributed parameter systems with arbitrary supporting conditions, is presented. The technique is based on the fact that the dynamic displacement of any point in a waveguide can be determined by superimposing the amplitudes of the wave components traveling along the waveguide, where the wave numbers of the constituent waves are defined in the Laplace domain instead of the frequency domain. The spatial amplitude variations of individual waves are represented by the field transfer matrix and the distortions of the wave amplitudes at point discontinuities due to constraints or boundaries are described by the wave reflection and transmission matrices. Combining these matrices in a progressive manner along the waveguide using the concepts of generalized wave reflection and transmission matrices leads to the exact transfer function of a complex distributed parameter system subjected to an externally applied force. The transient response solution can be obtained through the Laplace inversion using the fixed Talbot method. The exact frequency response solution, which includes infinite normal modes of the system, can be obtained in terms of the complex frequency response function from the system’s transfer function. This wave-based analysis technique is applicable to any one-dimensional viscoelastic structure (strings, axial rods, torsional bar, and beams), in particular systems with multiple point discontinuities such as viscoelastic supports, attached mass, and geometric/material property changes. In this paper, the proposed approach is applied to the flexural vibration analysis of a classical Euler–Bernoulli beam with multiple spans to demonstrate its systematic and recursive formulation technique.

A Transfer-Function Formulation For Nonuniformly Distributed Parameter Systems

1994 ◽  
Vol 116 (4) ◽  
pp. 426-432 ◽  
Author(s):  
B. Yang ◽  
H. Fang
Keyword(s):  
Transfer Function ◽  
State Space ◽  
Fundamental Matrix ◽  
Transfer Functions ◽  
Function Analysis ◽  
System Response ◽  
Approximate Methods ◽  
Arbitrary Boundary ◽  
Transfer Function Analysis ◽  
Function Formulation

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.

Transfer Functions of One-Dimensional Distributed Parameter Systems

1992 ◽  
Vol 59 (4) ◽  
pp. 1009-1014 ◽  
Author(s):  
B. Yang ◽  
C. A. Tan
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Distributed Parameter Systems ◽  
Axially Moving Beam ◽  
System Response ◽  
Distributed Parameter ◽  
One Dimensional ◽  
Adjoint Systems ◽  
The Laplace Transform ◽  
Axially Moving

Distributed parameter systems describe many important physical processes. The transfer function of a distributed parameter system contains all information required to predict the system spectrum, the system response under any initial and external disturbances, and the stability of the system response. This paper presents a new method for evaluating transfer functions for a class of one-dimensional distributed parameter systems. The system equations are cast into a matrix form in the Laplace transform domain. Through determination of a fundamental matrix, the system transfer function is precisely evaluated in closed form. The method proposed is valid for both self-adjoint and non-self-adjoint systems, and is extremely convenient in computer coding. The method is applied to a damped, axially moving beam with different boundary conditions.

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

1989 ◽  
Vol 256 (1) ◽  
pp. H142-H152 ◽  
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.

Distributed Transfer Function Analysis of Complex Distributed Parameter Systems

1994 ◽  
Vol 61 (1) ◽  
pp. 84-92 ◽  
Author(s):  
B. Yang
Keyword(s):  
Closed Form ◽  
Transfer Functions ◽  
Distributed Parameter Systems ◽  
Force Balance ◽  
Distributed Parameter ◽  
Distributed Parameter System ◽  
Parameter System ◽  
Lumped Parameter ◽  
Space Technique ◽  
Transfer Function Analysis

This paper presents a new analytical and numerical method for modeling and synthesis of complex distributed parameter systems that are multiple continua combined with lumped parameter systems. In the analysis, the complex distributed parameter system is first divided into a number of subsystems; the distributed transfer functions of each subsystem are determined in exact and closed form by a state space technique. The complex distributed parameter system is then assembled by imposing displacement compatibility and force balance at the nodes where the subsystems are interconnected. With the distributed transfer functions and the transfer functions of the constraints and lumped parameter systems, exact, closed-form formulation is obtained for various dynamics and vibration problems. The method does not require a knowledge of system eigensolutions, and is valid for non-self-adjoint systems with inhomogeneous boundary conditions. In addition, the proposed method is convenient in computer coding and suitable for computerized symbolic manipulation.

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

1991 ◽  
Vol 261 (4) ◽  
pp. H1231-H1245 ◽  
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.

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

1997 ◽  
Vol 83 (6) ◽  
pp. 2146-2157 ◽  
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.

Distributed Transfer Function Analysis of Ring-Stiffened Cylindrical Shells

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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