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 = = = + = u u x 2DOF systems (contd) 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 y x = = = = = = = = = = = = = = = 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 (contd) ) ( ) ( ) ( ) ( 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 = = + = = + i i i i T i i i T i i i i m k M K M K = = = 2 2 2 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 ) ( 1 2 = + . get , for solving after Finally, ) ( ) ( ) ( t U t t x = : EOMs modal to Transform uncoupled...
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ASE 365 - Lecture 18 - 2DOF systems EOMs from FBDs:...

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