Ch5-3(5-6)c - 1 MAE351 Mechanical Vibrations Lecture 23...

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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 bb l d t t d l l t 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 methods. • Recall from calculus that the minimum or maximum
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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 d fr dr d    2 () 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 nea min relative has )] , ( [ ) , ( ) , ( , 0 ) , ( If ) 1 2 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 ) , ( near 2 2 f r 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 point) 2 f r f r f r f rr r 22 2 2 2 2 2 2 0 ( ) ( ) aa a a a a a km c X F km k m m k k mm c     
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4 7 22 2 2 22 22 2 1 4 (, ) 4( 1 ) ( 1 ) where c/2 , / , / . pp r fr rr r r Jr J J     Lanchester (Houdaille) Damper - viscous absorber Shaft Casing 0, 0 21 2( 1)( 2) and 2 r ff Xk   Inertial disk( J 2 ) Viscous oil k x x a 0 max 1 M    Larger or larger absorber mass yields lower vibration of primary mass. Second order conditions can be resolved by the 3D plot of f ( r , ) when explicit derivations are troublesome. m m a F c a 8 3-dimensional plot of an objective function: Xk / M 0 = f ( , r ) for = 0.25 Each slice here is a 2-D is a 2 D magnitude plot for different ’s
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5 9 Example 5.5.1: Application of a viscous damper- mass absorber to the shaft of a rotating engine Given : J 1 =1.5 kg m 2 /rad, k 1 =6x10 3 Nm/rad, and a running (excitation) speed of 2000 rpm Design
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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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Ch5-3(5-6)c - 1 MAE351 Mechanical Vibrations Lecture 23...

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