Problem

A hard drive arm undergoes flow-induced vibration caused by the vortices of air produced b...

A hard drive arm undergoes flow-induced vibration caused by the vortices of air produced by a platter that rotates at ω0 = 10,000 rpm. The arm has length L = 0.037 m and mass m = 0.00075 kg, and it is made from aluminum with a modulus of elasticity E = 70 GPa. In addition, assume that the cross section of the arm has an area moment of inertia Ics = 8.5 × 10−14 m4. Following the steps in Example 9.2 on p. 682, the arm can be modeled as a rigid rod that is pinned at one end and is restrained by a torsional spring with equivalent spring constant kt = 3EIcs/L. In addition to the torsional spring, assume that the arm’s motion is affected by a torsional damper with torsional damping coefficient ct. Assuming that the damping ratio is ζ = 0.02 and that the vortices produce an aerodynamic force with the same frequency as the rotation of the platter, determine the amplitude of the aerodynamic force needed to cause a steady-state vibration amplitude of 0.0001 m at the tip of the arm. Assume that the aerodynamic force is applied at the midpoint B of the hard drive. What vibration amplitude will result if the same excitation is applied to a hard drive arm assembly with the damping ratio of 0.05?