SolSec 5.3 - 5- 21 Problems and Solutions Section 5.3 (5.27...

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5- 21 Problems and Solutions Section 5.3 (5.27 through 5.36) 5.27 A motor is mounted on a platform that is observed to vibrate excessively at an operating speed of 6000 rpm producing a 250-N force. Design a vibration absorber (undamped) to add to the platform. Note that in this case the absorber mass will only be allowed to move 2 mm because of geometric and size constraints. Solution: The amplitude of the absorber mass can be found from Eq. (5.22) and used to solve for k a : N/m 000 , 125 250 m 002 . 0 0 = = = = a a a a k k k F X From Eq. (5.21), ω π 2 2 2 125 000 6000 2 60 0 317 = == = k m m k a a a a , . k g
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5- 22 5.28 Consider an undamped vibration absorber with β = 1 and µ = 0.2. Determine the operating range of frequencies for which . 5 . 0 / 0 F Xk Solution: From Eq. (5.24), with β = ω ωω µ a p ap == = 1( ) i.e., and 0.2, Xk F a aa a 0 2 22 2 2 42 1 1 021 1 021 1 1 = + () − () = + .. . For 0 F Xk = 0.5, this yields 05 01 05 0 ... −= Solving for the physical solution gives a = 1 051 . Solving for a gives a = 0 955 1 813 ., . Comparing this to the sketch in Fig. 5.12, the values for which 0 F Xk 5 are 0 955 1 051 1 813 . a ≤≤ and
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5- 23 5.29 Consider an internal combustion engine that is modeled as a lumped inertia attached to ground through a spring. Assuming that the system has a measured resonance of 100 rad/s, design an absorber so that the amplitude is 0.01 m for a (measured) force input of 10 2 N. Solution: The amplitude of the absorber mass can be found from Eq. (5.22) and used to solve for k a : N/m 000 , 10 100 m 01 . 0 0 = = = = a a a a k k k F X Choose ω = 2 ω n = 200 rad/s. From Eq. (5.21), kg 25 . 0 200 000 , 10 2 2 = = = ω a a k m 5.30 A small rotating machine weighing 50 lb runs at a constant speed of 6000 rpm. The machine was installed in a building and it was discovered that the system was operating at resonance. Design a retrofit undamped absorber such that the nearest resonance is at least 20% away from the driving frequency.
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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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SolSec 5.3 - 5- 21 Problems and Solutions Section 5.3 (5.27...

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