A circular elastic shaft of length \(L\) has one end clamped and a rigid disk attached at the other end, as shown in Figure 7.53. If \(G\) denotes the modulus of rigidity, \(J\) the area polar moment of inertia of the shaft, \(I\) the mass polar moment of inertia of the shaft per unit length, and \(I_{D}\) the mass moment of inertia of the disk about its center axis, calculate the potential and kinetic energy expressions associated with the rotational motion, and derive the equation of motion using Lagrange's equation.

Transcribed Image Text:

ID GJ, I Figure 7.53: Torsional vibration of a shaft with a rigid disk.