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Ch5-3(5-6)c - 1 MAE351 Mechanical Vibrations Lecture...

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1 1 MAE351 Mechanical Vibrations Lecture 23 (Chap. 5.5-5.6) 2 5.5 Optimization of Vibration Absorber A certain amount of damping, which is expected to be able to improve the performance of vibration b b l d t t dl lt absorber, may lead to unexpectedly worse results. That is, damping is not necessarily beneficial. Design or choice of the best values for the absorber parameters (mass, stiffness and damping) can be formulated mathematically by using optimization methods. Recall from calculus that the minimum or maximum of a function of a single variable occurs where its
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2 3 Sports Dynamics: Archery 4 Swing Damper- damping device
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3 5 Optimization of a single variable 2 ( ) 0 min or max is achieved 0 min d f r dr d 2 ( ) f r dr Optimization of two variables For a function represented by f ( ζ , r ), critical points , where a min or max might occur, are given by . 0 ) , ( ) , ( 0 ) , ( ) , ( r f r f r r f r f r  6 ) ( near min relative has )] , ( [ ) , ( ) , ( , 0 ) , ( If ) 1 2 r f r f r f r f r f r rr   How to determine whether the critical points yield maximum or minimum? point) saddle a called is and max nor min neither has ) , ( ) , ( )] , ( [ If ) 3 ) , ( near max relative has )] , ( [ ) , ( ) , ( , 0 ) , ( If ) 2 , 2 2 f r f r f r f r f r f r f r f r f rr r r rr    properties these of any have could ) , ( ) , ( )] , ( [ If ) 4 2 f r f r f r f rr r  2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 ( ) ( )( ) ( ) a a a a a a a a a k m c X F k m k m m k k m m c
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