232x Filetype PDF File size 1.46 MB Source: ricopic.one
graphsLinear graph models intro Introduction to linear graphs p.1 graphs.intro Introduction to linear graphs 1 Engineersoftenusegraphicaltechniquesto linear graphs aid in analysis and design. We will use linear topology graphstorepresentthetopologyorstructure of a system modeled as interconnected lumped elements. 2 Thisrepresentstoustheessentialstructure of the system in a minimalist form. In this Q48 BUS TO LGA Mets-Willets Point M60 SBS Q48 BUS TO LGA M60 SBS TO LGA Q48 BUS TO LGA M60 SBS M60 SBS TO LGA LGA Airport TO LGA TO LGA Q72 BUS TO LGA Q3 BUS M60 SBS TO LGA Q47 BUS TO LGA Q70 SBS TO LGA TO JFK Q72 BUS Q10 TO LGA BUS Q70 SBS TO LGA TO JFK Q10 BUS TO JFK 7 Q10 BUS 1 2 3 7 N Q R W TO JFK JFK Airport L N Q R W B15 BUS TO JFK Figure intro.1: a modern New York subway map in the style of Vignelli (Jake Berman). graphsLinear graph models intro Introduction to linear graphs p.2 way,itis like Massimo Vignelli’s famous 1972 NewYorksubwaysystem“map,”which inspired widespread adoption of his style (see 1 1. Vignelli was a brilliant Minimalist designer of many prodcucts, Figure intro.1). Besides minimalism, the key fromdishestoclothing, but he was most known for his graphic design. idea in Vignelli subway maps is that the details Great places to start studying Vignelli are the documentary Design is One(2012)andTheVignelliCanon. of the tunnels’ paths are irrelevant and, in fact, distracting to the person attempting to get from onestation to another. 3 Inasimilarway,alineargraphrepresents the system in a minimalist style, with only two types of objects: edges 1. Asetofedges,eachofwhichrepresents anenergyportassociatedwithasystem element. Each edge is drawn as an oriented line segment “ ”. nodes 2. Asetofnodes,eachofwhichrepresents a point of interconnction among system elements. Each node is drawn as a dot “ ”. edge 4 Alledgesbeginandendatnodes. Thenodes V V V ref 1 2 represent locations in the system where distinct F node node across-variable values may be measured. For example, wires that connect elements Figure intro.2: an edge with nodes. The across variable is V = V1 −V2. are actually nodes at which voltage may be measured. Putting an edge together with nodes, wehaveFigureintro.2. 5 Itisimportanttonotethatlineargraphs nonlinearity canrepresent nonlinear system elements—the nameisareferencetothelinesused. 6 Itiscommontochooseanodeofthegraph reference node as the reference node, to which all across- variables are referenced. Due to its similarity to ground the electronic ground, we often use these terms interchangeably. 7 Figureintro.3showshowalineargraph canbeconstructedforasimpleRC-circuit. Notethatthewiresbecomenodes,the elements becomeedges,andthereference noderepresentsthecircuit ground. In a similar manner,wewillconstructlineargraphsof graphsLinear graph models sign Introduction to linear graphs p.3 circuits, mechanical translational systems, and mechanical rotational systems. R R + V − C s C V s Figure intro.3: an example of a linear graph representation of an RC-circuit.
no reviews yet
Please Login to review.