ASE 365 - Lecture 20 - Remember chapter 4? (Ignore shifting...

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Unformatted text preview: Remember chapter 4? (Ignore shifting and folding in text.) Convolution integral for response to arbitrary inputs Laplace transformstransfer function, ICs, delays Impulse, step, and ramp responses 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 F x x = + K M : EOMs with Begin coupled Ch. 52DOF systems 5.1 System configuration 5.2 EOMs of 2DOF systems 5.3 Free vibn of undamped systems 5.4 Response to initial excitations 5.5 Coordinate transformations & coupling 5.6 Orthogonality of modes, natural coords....
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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 at Austin.

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ASE 365 - Lecture 20 - Remember chapter 4? (Ignore shifting...

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