Ch4-5(7-8)c - 2009-03-17 1 MAE351 Mechanical Vibrations...

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2009-03-17 1 1 MAE351 Mechanical Vibrations Lecture 19 (Chap. 4.7-4.8) 2 4.7 Lagrange’s Equations ,..., 2 , 1 , n i Q q U q T q T dt d i i i i system, ve conservati a For coordinate th - i the at force d generalize : energy potential : energy, kinetic : where q W Q U T i i . Lagrangian the : where T-U L
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2009-03-17 2 3 Ex. 4.7.1 4 Ex. 4.7.2
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2009-03-17 3 5 Ex. 4.7.3 6 4.8 Examples (of multi-DOF systems) Ex. 4.8.1: Responses of a belt driven drive shaft to impulsive moment excitation J 1 = J 2 = J 3 =10kgm2/rad k 1 = k 2 = 10 3 Nm/rad c=2Nms/rad M(t): a unit impulse Initial conditions: zeroes
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2009-03-17 4 7 Equations of Motion ) ( ) ( ) ( ) ( ) ( ) ( 1 2 1 2 1 2 3 2 3 2 2 2 1 2 1 2 1 1 1 M c k J c k c k J c k J ) ( ) ( ) ( 2 3 2 3 2 3 3 t Define the vectors: or , ) ( 0 0 ) ( , 3 2 1 b t M t F x 11 1 21 1 2 2 32 2 00 0 0 ( ) 2 ( ) ( ) ( ) 0 0 Jc c k k J tc c c tk k k k t M t c k k      xx x b  8 EVP
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This note was uploaded on 02/11/2010 for the course MECHANICAL ms316 taught by Professor Abduljaba during the Spring '09 term at Kalamazoo.

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Ch4-5(7-8)c - 2009-03-17 1 MAE351 Mechanical Vibrations...

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