ASE 365 - Lecture 18

ASE 365 - Lecture 18 - 2DOF systems • EOMs from FBDs –...

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Unformatted text preview: 2DOF systems • EOMs from FBDs: – Matrices and vectors: – Coupling – Coordinate transformations • Undamped free vibration – Harmonic motion – Natural frequencies & modes – Response to nonzero ICs (modal): F x x x = + + K C M F F y x T T T T T KT T K CT T C MT T M T = ′ = ′ = ′ = ′ = , , , , ) ( ) sin cos ( ) ( 2 1 2 1 t t B t A t i i i i i i i i i η ϖ ϖ ∑ ∑ = = = + = u u x 2DOF systems (cont’d) • Orthogonality of modes w.r.t. M & K – Modal coordinate transformation [ ] [ ] [ ] ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 2 1 2 1 2 2 1 2 2 1 1 1 2 1 2 1 2 1 2 2 1 2 2 1 1 1 2 1 2 1 2 1 2 1 2 1 t t U t T t t k k K K K K K K m m M M M M M M t t t t U t T t T T T T T T T T T T T T T T T T i i i F u u F F F N u u u u u u u u u u u u u u u u u u u u u u u u u u u η y x = = = ′ = ′ ′ = = = ′ ′ ′ = = = ′ = = = = ∑ = η η η 1 2 2 1 1 2 2 1 u u u u u u u u K K M M T T T T = = = = , 2DOF systems (cont’d) ) ( ) ( ) ( ) ( 2 2 2 2 2 2 1 1 1 1 1 1 t t N k m t t N k m T T F u F u = = ′ + ′ = = ′ + ′ η η η η i i i i T i i i T i i i i m k M K M K ′ = ′ ⇒ = = 2 2 2 ϖ ϖ ϖ u u u u u u , From . at resonates mode So : EOM modal i th i i i i i th i t N m i ϖ η ϖ η ) ( 1 2 ′ = + . get , for solving after Finally, ) ( ) ( ) ( t U t t η x η = : EOMs modal to Transform uncoupled...
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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 18 - 2DOF systems • EOMs from FBDs –...

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