The piece of machinery shown in Figure 10.30 is mounted on a solid foundation in such a way that the mounting may be characterized as a rigid pivot and two stiff springs as shown. A damper is connected between the machine and an adjacent strong point. The mass of the machine is 500 kg, the length a = 1 m, the length b = 1.2 m and the spring stiffness is 8000Nm–1. The moment of inertia of the machine about the pivot point is 2ma². The machine generates internally a side-force F that may be approximated as F₀cos 2πft. As the machine runs up to speed, the frequency f increases from 0 to 6 Hz. What is the minimum damper coefficient that will prevent the machine from vibrating with any amplitude greater than twice its zero-frequency amplitude A(0) during a run-up?

Transcribed Image Text:

Effective pivot point a F b Figure 10.30 A compliantly mounted piece of machinery.