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.

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 Function Formulation of Constrained Distributed Parameter Systems, Part II: Applications

1993 ◽  
Vol 60 (4) ◽  
pp. 1012-1019 ◽  
Author(s):  
C. H. Chung ◽  
C. A. Tan
Keyword(s):  
Transfer Function ◽  
Elastic Foundation ◽  
Normal Modes ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Displacement Method ◽  
Mode Localization ◽  
Function Formulation ◽  
Free Beam ◽  
Symmetric Systems

In this paper, the application of the transfer function formulation and the generalized displacement method (GDM) to the analysis of constrained distributed parameter systems is illustrated. Two kinds of classical examples are considered. In the constrained free-free beam example, it is shown how the GDM gives the eigensolutions without requiring knowledge of the normal modes of the unconstrained beam. In the string on a partial elastic foundation example, mode localization and eigenvalue loci veering phenomena are examined. It is shown that mode localizaation can occur in spatially symmetric systems and for modes whose frequency loci do not veer.

The Normal Modes of Vibration of Certain Nonlinear Continuous Systems

1964 ◽  
Vol 31 (1) ◽  
pp. 139-140 ◽  
Author(s):  
Thein Wah
Keyword(s):  
Normal Modes ◽  
Distributed Parameter Systems ◽  
Structural Theory ◽  
Distributed Parameter ◽  
Continuous Systems ◽  
Simple Interpretation ◽  
Modes Of Vibration

Two examples from structural theory are invoked to show that “normal modes” of vibration could have a simple interpretation in nonlinear distributed parameter systems.

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.

Nature of coupling in non-conservative distributed parameter systems attached to external damping sources

2017 ◽  
Vol 25 (7) ◽  
pp. 1367-1383
Author(s):  
John Bellos ◽  
Daniel J Inman ◽  
Nikolaos Bakas
Keyword(s):  
Equations Of Motion ◽  
Normal Modes ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Modal Coupling ◽  
Theoretical Predictions ◽  
Coupling Parameters ◽  
The Mathematical Model ◽  
Euler Bernoulli Beam ◽  
Response Errors

Non-conservative distributed parameter systems connected to external damping sources and possessing non-normal modes are analyzed in this work. The mathematical model of such systems is presented and real valued modal analysis is used to obtain the coupled modal equations of motion. A decoupling technique is developed using Fourier expansion, fictitious damping ratios, modal coupling parameters and pseudo forces. The method is applicable to all types of excitation. A normal mode criterion in the form of non-proportionality indices is also provided. The theoretical predictions are verified through application to a non-conservative Euler–Bernoulli beam with non-proportional damping configuration and various types of boundary conditions. Numerical examples emphasize the response errors associated with the proportional damping assumption and reveal the advantages of the proposed approach over the exact method.

scholarly journals A new method for determination of the reliability index of distributed parameter systems

2003 ◽  
Vol 25 (4) ◽  
pp. 255-262
Author(s):  
Nguyen Van Pho
Keyword(s):  
Distributed Systems ◽  
Density Function ◽  
Reliability Index ◽  
Mechanical Systems ◽  
Distributed Parameter Systems ◽  
New Method ◽  
Distributed Parameter

In this paper, a method to determine the reliability - index of distributed systems is proposed. By the new method, instead of finding jointly probability depending on multi - conditions of inequalities one can find probability depending on only one inequality and no requiring to know jointly density function of basic variables. Therefore, it is very favourable for the calculation of the reliability - index of mechanical systems with distributed parameter. For illustrating the proposed method, a simple example is considered

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.

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