Ch1-4(7-10)c - MAE351 Mechanical Vibrations Lecture 4...

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1 MAE351 Mechanical Vibrations Lecture 4 (Chap. 1.7-1.10) 2 Design Considerations (Section 1 7 (Section 1.7) Using the analysis so far to guide the selection of components.
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2 Example 1.7.1: design of damper for varying mass system Mass 2 kg < m < 3kg and k > 200 N/m 3 • Mass 2 kg < m < 3kg and > 200 N/m • For a possible frequency range of 8.16 rad/s < n < 10 rad/s • For initial conditions: x 0 = 0, v 0 < 300 mm/s • Choose a c so that response is always < 25 mm Solution: • Write down x ( t ) for 0 initial 1 4 for 0 initial displacement • Look for max amplitude occurs at time of first peak ( T max ) • Compute the -0.5 0 0.5 Amplitude amplitude at T max • Compute for A ( T max )=0.025 0 0.5 1 1.5 2 -1 Time(sec)
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3 0 Amplitude 0 0 () s in ( ) worst case happens at smallest 8.16 rad/s worst case happens at max 300 mm/s With and fixed at these values, investigate how x varies with n t d d dn n v xt e t v v        5 First p  2 1 2 11 max 1 t( ) eak is highest and occurs at 0 cos ( ) s ( ) 0 1 Solve for tan ( ) tan nn tt dd n d d m d d e t e t dt tT T        2 tan 1 1 0 max 2 1 Sub into ( ): ( ) ( ) sin(tan 1 mm n v Tx t A x T e  2 1 2 2 1 tan ( ) 1 0 ) ( ) m n v Ae To keep the max value less then 0.025 m solve A max ( ) 0.025 0.281 6 Using the upper limit on the mass ( m = 3 kg) yields c 2 3 8.16 0.281 14.15 kg/s FYI, = 0 yields A max v 0 n
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4 Example 1.7.3 What happens to a good design when someone changes the parameters? (ex. Car suspension system). How does change with mass? 7 Given =1, m =1361 kg, = 0.05 m, compute c , k . n k m k 1361 n 2 mg k  k mg n mg m 9.81 0 05 14 rad/s 0.05 k 1361(14) 2 =1 c 2 m n 2(1361)(14) Now add 290 kg of passengers and luggage. What happens? m 1361 290 1651 kg 8  mg k 1651 9.8 2.668 10 5 0.06 m n g 9.8 0.06 c c cr 3.81 10 4 2 m n So some oscillation results at a lower frequency.
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5 1.8 Stability x k x c x x f t kx t x c t x m 1 1 ) , ( ) ( ) ( ) ( k f Displacement 9 M c What would happen when c < c 1 and k < 1 ?
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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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Ch1-4(7-10)c - MAE351 Mechanical Vibrations Lecture 4...

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