July 2011

Engineering Case Histories

Case 63: Analyzing off resonance amplitudes

It is important to know the amplitudes of vibration away from resonance

Sofronas, A., Consulting Engineer

Resonance or the critical speed describes the condition at which the force action, torque or moment is the same as the resonance frequency or speed at which resonance occurs. When this “sameness” happens, large amplitudes can develop. Often, the system is designed away from this resonance point. Here is a case where a vibration developed and a quick look at the critical speed was desired. Fig. 1 shows the simple rotor of a steam turbine; the rotor was lumped into a single mass system. The first bending critical speed or natural frequency of such a simply supported shaft, and whose mode shape is shown by the dashed line, is: fn = 1,300 3 (E 3 I /(W 3 L3) )1⁄2 cycles/min or

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