ASE 365 - Lecture 24

# ASE 365 - Lecture 24 - “Prototype” MDOF system FBDi mi...

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Unformatted text preview: “Prototype” MDOF system: FBDi mi Fi fS, i fD, i fD, i+1 fS, i+1 { } 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 , 1 , , , ) ( ) ( ) ( ) ( ) ( ) ( + + +- + + +- + + + +-- + +- + +-- + +-- =- +- +---- = + +-- = i i i i i i i i i i i i i i i i i i i i i i i i i i i i i D i S i D i S i i i x k x k k x k x c x c c x c F x x c x x k x x c x x k F f f f f F x m k 1 c1 m 1 F1 c2 m 2 k 2 F2 x2 x 1 c3 m 3 k 3 F3 x3 c4 m 4 k 4 F4 x4 c5 k 5 = +-- +-- +-- + + +-- +-- +-- + + 4 3 2 1 4 3 2 1 5 4 4 4 4 3 3 3 3 2 2 2 2 1 4 3 2 1 5 4 4 4 4 3 3 3 3 2 2 2 2 1 4 3 2 1 4 3 2 1 F F F F x x x x k k k k k k k k k k k k k k x x x x c c c c c c c c c c c c c c x x x x m m m m : form Matrix Lagrangian approach: 2 4 5 2 1 2 3 4 4 2 1 2 2 3 3 2 1 2 1 2 2 2 1 2 1 1 2 1 2 4 4 2 1 2 3 3 2 1 2 2 2 2 1 2 1 1 2 1 ) ( ) ( ) ( x k x x k x x k x x k x k V x m x m x m x m T +- +- +- + = + + + = k 1 c1 m 1 F1 c2 m 2 k 2 F2 x2 x 1 c3 m 3 k 3 F3 x3 c4 m 4 k 4 F4 x4 c5 k 5 : , nc i W δ For mi Fi fD, i fD, i+1 δxi i i i i i i i i i i i i D i i D i i nc i x x x c x x x c x F x f x f x F W δ δ δ δ δ δ δ )} ( { )} ( { 1 1 1 1 , , , - +-- = +- = + +- + 4 4 5 3 4 4 4 3 3 4 4 2 3 3 3 2 2 3 3 1 2 2 2 1 1 2 2 1 1 1 } ) ( { )} ( ) ( { )} ( ) ( { )} ( { x x c x x c F x x x c x x c F x x x c x x c F x x x c x c F W nc δ δ δ δ δ --- +- +-- +- +-- +- +- = nc j j j j Q q V q T q T dt d , = ∂ ∂ + ∂ ∂- ∂ ∂ : equations s Lagrange' ( 29 ) ( ) ( ), ( ) ( , , 1 1 1 , 1 1 1 i i i i i i i nc i i i i i i i i i i i i i i x x c x x c F Q x x k x x k x V x T x m x m dt d x T dt d - +-- =--- = ∂ ∂ = ∂ ∂ = = ∂ ∂ + +- + +- ) ( ) ( ) ( ) ( 1 1 1 1 1 1 i i i i i i i i i i i i i i i x x c x x c F x x k x x k x m i - +-- =--- + + +- + +- : EOM th i i i i i i i i i i i i i i i...
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## This note was uploaded on 09/18/2011 for the course ASE 365 taught by Professor Staff during the Spring '10 term at University of Texas.

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ASE 365 - Lecture 24 - “Prototype” MDOF system FBDi mi...

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