Question

Vibrations

A steel shaft of diameter d and length I is fixed at one end and carries a propeller of mass m and aradius of gyration of r, at the other end (see Figure 1).

Data: d = 5 cm,l=1m, m = 100 kg, r, = 10 cm

1- Determine the fundamental natural frequeney of vibration of the shaft in axial vibration

Determine the fundamental natural frequency of vibration of the shaft in torsional

Task 1.3- Is it possible to change the system parameters (d, l, m, r,) such that the fundamentalfrequencies for both axial and torsional vibration become identical?[30%]

If yes, what are the new parameter values? Explain the method and report your detailedanalysis leading to the new values.

If no, explain in detail why it is impossible.

I.Note 1: In Tasks 1.1 and 1.2, derive boundary conditions, start from the relevant equation of motionand apply the boundary conditions, find characteristic equation, solve it for natural frequencies, andfind the fundamental frequency.


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