An Augmented State Formulation for Modeling and Analysis of Multibody Distributed Dynamic Systems

2014 ◽  
Vol 81 (5) ◽  
Author(s):  
K. Noh ◽  
B. Yang
Keyword(s):  
Distributed Systems ◽  
Transfer Function ◽  
Dynamic Systems ◽  
Analytical Method ◽  
Dynamic Problems ◽  
Modeling And Analysis ◽  
Closed Form Solutions ◽  
Time Domains ◽  
Augmented State ◽  
Distributed Transfer Function

Multibody distributed dynamic systems are seen in many engineering applications. Developed in this investigation is a new analytical method for a class of branched multibody distributed systems, which is called the augmented distributed transfer function (DTFM). This method adopts an augmented state formulation to describe the interactions among multiple distributed and lumped bodies, which resolves the problems with conventional transfer function methods in modeling and analysis of multibody distributed systems. As can be seen, the augmented DTFM, without the need for orthogonal system eigenfunctions, produces exact and closed-form solutions of various dynamic problems, in both frequency and time domains.

Port-Based Modeling of Distributed-Lumped Parameter Systems

2010 ◽  
Vol 164 ◽  
pp. 183-188
Author(s):  
Cezary Orlikowski ◽  
Rafał Hein
Keyword(s):  
Distributed Systems ◽  
Transfer Function ◽  
Distributed System ◽  
Function Method ◽  
Input Data ◽  
Distributed Parameter ◽  
Transfer Function Method ◽  
Lumped Parameter ◽  
Concise Representation ◽  
Distributed Transfer Function

This paper presents a uniform, port-based approach for modeling of both lumped and distributed parameter systems. Port-based model of the distributed system has been defined by application of bond graph methodology and distributed transfer function method (DTFM). The proposed approach combines versatility of port-based modeling and accuracy of distributed transfer function method. A concise representation of lumped-distributed systems has been obtained. The proposed method of modeling enables to formulate input data for computer analysis by application of DTFM.

A Space Function Approach to the Hyperstability and the Average Hyperstability of Distributed Systems With Space-Varying Linear Parts and Time-Varying Gains

1975 ◽  
Vol 97 (4) ◽  
pp. 345-353 ◽  
Author(s):  
G. Jumarie
Keyword(s):  
Distributed Systems ◽  
Transfer Function ◽  
Broad Class ◽  
Linear Part ◽  
Function Approach ◽  
Distributed Parameter ◽  
Time Varying ◽  
Function Concept ◽  
Distributed Transfer Function ◽  
Hyperstability Theory

We propose an extension of the Popov’s hyperstability theory which applies to a class of single-control distributed systems in which the linear part depends explicitely upon the distributed parameter, z. The nonlinearness of these systems is expressed by means of the control. The main features of our results are the following: (i) The hyperstability conditions that we obtain involve specific z-dependent functions which we can consider as being extensions of the transfer function concept; (ii) they also involve integrals with respect to the distributed parameter, which express an averaging effect of this latter. Then systems in which the admissible controls are defined via time-varying conditions are investigated. For such systems, we define the concept of “average hyperstability” in time, and average hyperstability conditions are given. Similar problems are solved for multi-control distributed systems. As an application we show how these results yield a broad class of absolute stability conditions for distributed systems: they are space averaging conditions and they may apply when other criteria are in-applicable. Three examples are given: the last one illustrates how a space-describing function approach can be used to determine the distributed transfer function of the system.

A Closed-Form Approach to Transient Dynamic Response of One-Dimensional Distributed Systems

1999 ◽  
Author(s):  
Xuqiang Wu ◽  
Bingen Yang
Keyword(s):  
Transfer Function ◽  
Closed Form ◽  
Dynamic Systems ◽  
Transient Analysis ◽  
Inverse Laplace Transform ◽  
External Boundary ◽  
Modal Expansion ◽  
One Dimensional ◽  
Distributed Transfer Function ◽  
Form Approach

Abstract A closed-form transient analysis of one-dimensional distributed dynamic systems is presented. The proposed approach, called the Z-Prime Method, starts with inverse Laplace transform of a distributed transfer function formulation. Through establishment of a relation between transfer function residues and system eigensolutions, the closed-form transient response of the distributed system under general external, boundary and initial disturbances is obtained. Unlike conventional modal expansion, the proposed method does not depends on any orthogonal eigenfunctions.

Distributed Transfer Function Synthesis of Multi-Body Flexible Rotor Systems

1997 ◽  
Author(s):  
Bingen Yang ◽  
Houfei Fang
Keyword(s):  
Transfer Function ◽  
Analytical Solutions ◽  
General Boundary Conditions ◽  
Flexible Rotor ◽  
Modeling And Analysis ◽  
Numerical Examples ◽  
Rotor Systems ◽  
Distributed Transfer Function ◽  
Multi Body ◽  
Flexible Rotor Systems

Abstract A distributed transfer function synthesis is proposed for modeling and analysis of rotor systems assembled from multiple flexible and rigid components. The method is capable of treating non-self-adjoint effects, general boundary conditions and multi-body coupling, and delivers exact and closed-form analytical solutions for various problems. The proposed method is illustrated in two numerical examples.

SEMI-ANALYTICAL SOLUTION OF TWO-DIMENSIONAL ELASTICITY PROBLEMS BY FINITE DIFFERENCE–DISTRIBUTED TRANSFER FUNCTION METHOD

2010 ◽  
Vol 10 (02) ◽  
pp. 315-334 ◽  
Author(s):  
YAUBIN YANG ◽  
BINGEN YANG
Keyword(s):  
Transfer Function ◽  
Finite Difference ◽  
Analytical Solution ◽  
Function Method ◽  
Transfer Functions ◽  
Two Dimensional ◽  
Dynamic Problems ◽  
Arbitrary Boundary ◽  
Transfer Function Method ◽  
Distributed Transfer Function

A semi-analytical solution method, called the Finite Difference–Distributed Transfer Function Method, is developed for static and dynamic problems of two-dimensional elastic bodies composed of multiple rectangular subregions. In the development, the original two-dimensional elasticity problem is first reduced into a one-dimensional boundary-value problem by finite difference; the exact solution of the reduced problem is then obtained by using the distributed transfer functions of the elastic continuum. The proposed technique, which combines the simplicity of finite difference and the closed form of analytical solutions, is capable of handling arbitrary boundary conditions, delivers highly accurate solutions for static and dynamic problems, and is computationally efficient. The proposed method is illustrated on a square region and an L-shaped region.

A Stochastic Hierarchical Population System: Excitement, Extinction and Transition to Chaos

2021 ◽  
Vol 31 (14) ◽  
Author(s):  
Irina Bashkirtseva ◽  
Tatyana Perevalova ◽  
Lev Ryashko
Keyword(s):  
Mathematical Modeling ◽  
Food Chain ◽  
Analytical Method ◽  
Three Dimensional ◽  
Biological Parameters ◽  
Top Predator ◽  
Population System ◽  
Modeling And Analysis ◽  
Transition To Chaos ◽  
Random Fluctuations

A problem of the mathematical modeling and analysis of noise-induced transformations of complex oscillatory regimes in hierarchical population systems is considered. As a key example, we use a three-dimensional food chain dynamical model of the interacting prey, predator, and top predator. We perform a comparative study of the impacts of random fluctuations on three key biological parameters of prey growth, predator mortality, and the top predator growth. A detailed investigation of the stochastic excitement, noise-induced transition from order to chaos, and various scenarios of extinction is carried out. Constructive abilities of the semi-analytical method of confidence domains in the analysis of the noise-induced extinction are demonstrated.

scholarly journals Compositional Verification using Model Checking and Theorem Proving

2020 ◽  
pp. 305-314
Author(s):  
Diego Marmsoler
Keyword(s):  
Distributed Systems ◽  
Model Checking ◽  
Embedded Systems ◽  
Theorem Proving ◽  
Formal Modeling ◽  
Compositional Verification ◽  
Modeling And Analysis ◽  
Simple Version ◽  
Evolving Systems ◽  
Alternative Approach

AbstractCollaborative embedded systems form groups in which individual systems collaborate to achieve an overall goal. To this end, new systems may join a group and participating systems can leave the group. Classical techniques for the formal modeling and analysis of distributed systems, however, are mainly based on a static notion of systems and thus are often not well suited for the modeling and analysis of collaborative embedded systems. In this chapter, we propose an alternative approach that allows for the verification of dynamically evolving systems and we demonstrate it in terms of a running example: a simple version of an adaptable and flexible factory.

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