The vector-network model: A new approach to vector dynamics

Andrews, Gordon C.; Kesavan, H. K.

doi:10.1016/0094-114x(75)90057-9

Cited by 79 publications

(47 citation statements)

References 7 publications

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“…It should be acknowledged that the use of graphs to represent system topology during the generation of the governing equations of motion in multi-body dynamic systems has been exploited by Andrews and his coworkers [97][98][99][100], Sheth and Uicker [101] and by Wittenburg [102,103]. In Wittenburg's graph rigid bodies represent not only graph vertices and the edges of the kinematic pairs, but also spring-damper elements.…”

Section: Dynamic Analysis and Simulation Of Multi-body Systemsmentioning

confidence: 99%

On Crossley's contribution to the development of graph based algorithms for the analysis of mechanisms and gear trains

Pennestrı̀

Belfiore

2015

Mechanism and Machine Theory

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This paper celebrates a particular branch of Crossley's early work dedicated to Mechanism Science, which deals with a rigorous introduction of Graph Theory to the study of some fundamental and intrinsic properties of kinematic chains and mechanisms. Although such idea gave its main outcome in Type and Number Synthesis (which has been much better and extensively described in another paper of the present special issue) some other intriguing side effects appeared, later in Mechanism Science, which yielded several results, and are still in the center of research and industrial world interest, such as, to name but a few, the automatic generation of the equations governing kinematic, static force and dynamic analysis of mechanisms and geared trains, the power flow analysis, the computation of the efficiency and, finally, the never fully explored structure-to-function mapping, which the present contribution points out to be still a challenge in the field

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Section: Dynamic Analysis and Simulation Of Multi-body Systemsmentioning

confidence: 99%

On Crossley's contribution to the development of graph based algorithms for the analysis of mechanisms and gear trains

Pennestrı̀

Belfiore

2015

Mechanism and Machine Theory

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“…This arrangement is called a chord transformation (Roe , 1966;Andrews and Kesavan , 1975;McPhee et al , 2004;McPhee , 1996McPhee , , 1998 and can be mathematically expressed as…”

Section: Overviewmentioning

confidence: 99%

“…Linear graph theory is a branch of mathematics that studies the manipulation of topology (Roe , 1966;Andrews and Kesavan , 1975). Although this theory has been extensively incorporated into formulation of a wide range of physical systems, namely electrical, mechanical, and hydraulic systems, the extent to which this theory has been applied to modeling electrochemical and thermal processes remains from nil to minimum.…”

Section: Introductionmentioning

confidence: 99%

Dynamic modeling of electrochemical systems using linear graph theory

Dao

McPhee

2011

Journal of Power Sources

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An electrochemical cell is a multidisciplinary system which involves complex chemical, electrical, and thermodynamical processes. The primary objective of this paper is to develop a linear graph-theoretical modeling for the dynamic description of electrochemical systems through the representation of the system topologies. After a brief introduction to the topic and a review of linear graphs, an approach to develop linear graphs for electrochemical systems using a circuitry representation is discussed, followed in turn by the use of the branch and chord transformation techniques to generate final dynamic equations governing the system. As an example, the application of linear graph theory to modeling a nickel metal hydride (NiMH) battery will be presented. Results show that not only the number of equations are reduced significantly, but also the linear graph model simulates faster compared to * Corresponding author Email addresses: tdao@maplesoft.com (Thanh-Son Dao), mcphee@real.uwaterloo.ca (John McPhee) Preprint submitted to Power SourcesAugust 6, 2011 *Manuscript text (double-spaced) Click here to view linked ReferencesThe final publication is available at Elsevier via http://dx.doi.org/10.1016/j.jpowsour.2011.08.065 © 2011 the original lumped parameter model. The approach presented in this paper can be extended to modeling complex systems such as an electric or hybrid electric vehicle where a battery pack is interconnected with other components in many different domains.

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“…The use of graph theory in engineering is well known, and this paper employs some of the results developed in the various engineering disciplines, such as: electricity -the works of Kron (1963), Seshu and Reed (1961) and others for representing and analysis of electrical circuits; In machine theory -the graphs were used to represent linkages and gear trains for analysis or enumeration, such as: Freudenstein (Dobrjanskyj and Freudenstein, 1967;Freudenstein and Maki, 1979), Tsai (Tsai et al, 1998); in dynamics the graphs that were used to represent multidimensional dynamic systems upon which to perform the analysis (Andrews, 1971;McPhee, 1996); in structural mechanics -network graphs were studied in order to develop computer software for analysis (Fenves and Branin, 1963) who implemented the first computer program from the network topology and graph algorithms (Fenves et al, 1965).…”

Section: Graph Representations and Relations Between Themmentioning

confidence: 99%

Graph theoretical duality perspective on conjugate structures and its applications

Ta'aseh

Shai

2005

European Journal of Mechanics - A/Solids

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The paper shows that representing structures, beams and frames by mathematical models based on graph theory enables to provide new perspective on known conjugate structure theorems in mechanics. It is shown that the latter theorems can be derived from the graph theoretical duality principle applied upon the graph representations of the structures. The results reported indicate upon theoretical value of the approach, as the established mathematical foundation can be employed in a variety of mechanical disciplines.  2005 Elsevier SAS. All rights reserved.

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The vector-network model: A new approach to vector dynamics

Cited by 79 publications

References 7 publications

On Crossley's contribution to the development of graph based algorithms for the analysis of mechanisms and gear trains

On Crossley's contribution to the development of graph based algorithms for the analysis of mechanisms and gear trains

Dynamic modeling of electrochemical systems using linear graph theory

Graph theoretical duality perspective on conjugate structures and its applications

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