Transfer Functions of Hyperbolic Distributed Parameter Systems

1976 ◽  
Vol 98 (3) ◽  
pp. 318-319 ◽  
Author(s):  
A. K. Sen
Keyword(s):  
Distributed Systems ◽  
Analytical Methods ◽  
Transfer Functions ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
New Class

Concepts and analytical methods of construction of transfer functions of linear hyperbolic distributed systems are developed. In addition to the usual class of problems with boundary inputs, an important new class of problems with internal inputs is discussed.

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.

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.

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.

Optimum Control of Distributed-Parameter Systems

1964 ◽  
Vol 86 (1) ◽  
pp. 67-79 ◽  
Author(s):  
P. K. C. Wang ◽  
F. Tung
Keyword(s):  
Distributed Systems ◽  
Dynamical Systems ◽  
Maximum Principle ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Control Problems ◽  
Optimum Control ◽  
Linear Diffusion ◽  
One Dimensional ◽  
Controllability And Observability

This paper presents a general discussion of the optimum control of distributed-parameter dynamical systems. The main areas of discussion are: (a) The mathematical description of distributed parameter systems, (b) the controllability and observability of these systems, (c) the formulation of optimum control problems and the derivation of a maximum principle for a particular class of systems, and (d) the problems associated with approximating distributed systems by discretization. In order to illustrate the applicability of certain general results and manifest some of the properties which are intrinsic to distributed systems, specific results are obtained for a simple, one-dimensional, linear-diffusion process.

The Nature of the Temporal Solutions of Damped Distributed Systems With Classical Normal Modes

1982 ◽  
Vol 49 (4) ◽  
pp. 867-870 ◽  
Author(s):  
D. J. Inman ◽  
A. N. Andry
Keyword(s):  
Distributed Systems ◽  
Normal Modes ◽  
Distributed Parameter Systems ◽  
Time Response ◽  
Distributed Parameter

Conditions under which the time response of certain distributed parameter systems, which are assumed to possess “classical normal” modes, is critically damped, overdamped, or underdamped are presented. The conditions are derived from the definiteness of certain combinations of the coefficient operators of the describing equations. These conditions are compared to previous results and their usefulness is illustrated by examples.

Discrete-Time Models and Stability of Distributed Parameter Systems

1967 ◽  
Vol 89 (2) ◽  
pp. 327-333 ◽  
Author(s):  
D. C. Garvey ◽  
A. F. D’Souza
Keyword(s):  
Discrete Time ◽  
Transfer Functions ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Time Model ◽  
Closed Loop Systems ◽  
Distributed Parameters ◽  
Analysis And Synthesis ◽  
The Stability ◽  
Linear And Nonlinear Systems

The partial differential equations describing distributed parameter systems may often be reduced to transcendental transfer functions with the aid of appropriate boundary conditions. In the analysis and synthesis of closed loop systems, the transcendental transfer functions have to be approximated in a suitable manner. In this paper, discrete-time model of distributed parameter systems is obtained. The model employs a sample and hold circuit in the loop. The response of the model system is compared with the response obtained by approximating the transcendental transfer function by root factor and other approximations. The stability of linear and nonlinear systems with distributed parameters is investigated by employing the Mikhailov stability criterion.

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