Question

A flexible machine part was observed to vibrate excessively at 20 Hz due to a harmonic force of unknown amplitude. It was concluded that vibration was large because the harmonic force coincided with the natural frequency of the flexible part.

When the harmonic force was not present, a 0.5 kg mass was placed on the flexible part and a static displacement of 3.0 mm was observed. The mass was then removed.

a) The flexible part is to be modelled as a one degree-of-freedom, mass-spring-damper system. What mass and stiffness would be appropriate?

b) A tuned vibration absorber is used to eliminate the vibration at 20 Hz. If a mass of 0.03 kg is used for the absorber, what stiffness is required?

c) If the amplitude of the absorber mass at 20 Hz was observed to be1 cm, what is the amplitude of the harmonic force acting on the flexible part?

Answer 1

a) Static deflection for 0.5 kg mass is

Hence stiffness of flexible part is

Natural frequency is 20 Hz(resonant frequency)

Hence

Or

Or

b) For complete elemination of vibration at 20 Hz, the absorber mass is given by

Or

or

c) The exciting force is given by the relation

X₂= amplitude of absormer mass = 0.01 m

F= exciting force on flexible main part.

Hence