University of Florida/Egm6341/s11.TEAM1.WILKS/Mtg1

EGM6321 - Principles of Engineering Analysis 1, Fall 2010
Mtg 1: Tue, 24 Aug 10

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- course website, wiki - high-speed trains German transrapid (electromagentic attraction) Japanese MAglev (electrodynamic repulsion) Grench TGV (wheel on rail) Vu Quoc and Olsson 1989 CMAME vehicle/structure interaction, where vehicle is the high speed maglev and the structure is the the flexible guideway



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$$ Y^1(t)= \ $$ nominal position of wheel (w/o guideway definition) $$ S=x^1 \ $$, horizontal coordinate $$u^1 (S,t)= \ $$ axial deformation (displacement) of guideway, where $$t \ $$ is the time parameter $$u^2 (S,t)= \ $$ transverse deformation (displacement) of guideway $$u^2_{,s}:=\frac{\partial u^2(s,t)}{\partial S} \ $$, where := means equal by definition (non symmetric) NOTE: $$ \Delta\ $$ and def are symbols (no direction) $$ A:=B \ $$ means A is defined by B

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$$ A=:B \ $$ means B is defined by A Axial displacement under moving wheel/magnet $$ =u^1(Y^1(t),t) \ $$ Where $$ s=y^1(t) \ $$ General setting: $$ f(S,t) \ $$, where $$ S=Y^1(t) \ $$ where $$ \dot y ^1 = \frac{dY^1}{dt} $$ Where $$ f_{,s}(Y^1,t)=\frac{\partial f}{\partial S} \ $$ and $$ f_{,ss}(Y^1,t)=\frac{\partial ^2f}{\partial S^2} \ $$