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Engineering and Tech / System Dynamics 3 / Chapter 9 / Problem 9.20

System Dynamics | 3rd Edition | ISBN: 9780073398068 | Authors: William J Palm III

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QUESTION:

A certain factory contains a heavy rotating machine that causes the factory floor to vibrate. We want to operate another piece of equipment nearby and we measure the amplitude of the floor’s motion at that point to be 0.01 m. The mass of the equipment is 1500 kg and its support has a stiffness of \(k=2 \times 10^{4} \mathrm{~N} / \mathrm{m}\) and a damping ratio of \(\zeta=0.04\). Calculate the maximum force that will be transmitted to the equipment at resonance.

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QUESTION:

A certain factory contains a heavy rotating machine that causes the factory floor to vibrate. We want to operate another piece of equipment nearby and we measure the amplitude of the floor’s motion at that point to be 0.01 m. The mass of the equipment is 1500 kg and its support has a stiffness of \(k=2 \times 10^{4} \mathrm{~N} / \mathrm{m}\) and a damping ratio of \(\zeta=0.04\). Calculate the maximum force that will be transmitted to the equipment at resonance.

ANSWER:

Step 1 of 2

The damping constant is given by,

Substitute for , for and for in the above equation.

The resonant frequency is given by,

for

The other form of resonant frequency is given by,

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