Ch5-2(3-4)c

# Ch5-2(3-4)c - 1 MAE351 Mechanical Vibrations Lecture...

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1 1 MAE351 Mechanical Vibrations Lecture 22 (Chap. 5.3-5.4) 2 Coupled oscillator Vibration absorber f=0.67 f=1.0 f=1.3 (Courtesy of Dr. D. Russell)

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2 3 5.3 Vibration Absorbers Primary mass m x F ( t )= 0 sin Primary system experiences resonance (Excitation absorber m a k a x a K /2 K /2 • Primary system experiences resonance (Excitation frequency may not necessarily be equal to natural frequency of the primary system). • Add a secondary (absorber) system as indicated. • Look at equations of motion (now 2-DOF). 4 Equations of Motion 0 sin 0 0 0 t F x x k k k k k x x m m a a sin ) ( sin ) ( : solution state steady a Assume t X t x t X t x a a a a a a a 0 0 2 2 F X X m k k k m k k a a a a a a
3 5 0 1 2 2 0 a a F m k k k m k k X X 2 2 2 0 2 ) )( ( ) ( a a a a a a a a a a F k k m k m k k F m k X Pick m a and k to make the numerator or deflection of the primary 2 2 2 0 ) )( ( a a a a a a k m k m k k X system zero. All the system motion goes into the absorber mass. 6 2 k a Choose the absorber mass & stiffness from: 0 0 0 of magnitude force a sin ) ( F k F k x k t k F t x m a a a a a a a and the absorber mass to oscillate at: As in case of the isolator, static deflection, rattle space and force magnitudes need to be checked in each design.

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4 7 Other pitfalls in absorber design • Exact tuning of the absorber frequency with the excitation frequency is essential excitation frequency is essential. • A single frequency device. •I f shifts, it could end up with exciting at one of the natural frequencies of the combined system (resonance). •Damping, which always exists to some degree in every real system, can spoil the absorption. 8 Avoidance of resonance (robustness) m a Mass ratio m p k m a k a m a k 2 Original natural frequency of primary system before absorber is attached Natural frequency of absorber before it is attached to primary mass a
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Ch5-2(3-4)c - 1 MAE351 Mechanical Vibrations Lecture...

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