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

$u_{,s}^2:=\frac{\partial u^2(s,t)}{\partial S}$, where := means equal by definition (non symmetric)

NOTE: $\mathrm{\Delta }$ 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 $=u^1(Y^1(t),t)$

$\begin{array}{c}{u}^1(S,t)\end{array}$

Where $s=y^1(t)$

General setting: $f(S,t)$, where $S=Y^1(t)$

$\begin{array}{c}=f(Y^1(t),t)\end{array}$

$\begin{array}{c}\frac{d}{dt}f(Y^1(t),t)=\frac{\partial f(Y^1(t),t){\dot{y}}^1}{\partial S}+\frac{\partial f(Y^1(t),t)}{\partial t}\end{array}$

where ${\dot{y}}^1=\frac{d{Y}^1}{dt}$

$\begin{array}{c}\frac{d^{2}f}{d{t}^2}=f_{,s}(Y^1,t){\ddot{y}}^1+f_{,ss}({\dot{y}}^1{)}^2+2f_{,st}{\dot{y}}^1+f_{,tt}\end{array}$

Where $f_{,s}(Y^1,t)=\frac{\partial f}{\partial S}$

and $f_{,ss}(Y^1,t)=\frac{{\partial }^{2}f}{\partial S^2}$

References

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