The critical speed of a rotating shaft is the theoretical angular velocity at which the shaft begins to resonate violently. Resonance occurs when the frequency of an external force matches the natural frequency of the shaft. At the critical speed, even a small amount of imbalance in the shaft can cause large deflections and vibrations, potentially leading to catastrophic failure. The critical speed depends on the shaft's physical properties, including its length, diameter, material, and support conditions. The calculation of the critical speed involves determining....
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