A steel shaft of diameter d and length I is fixed at one end and carries...

 

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A steel shaft of diameter d and length I is fixed at one end and carries a propeller of mass m and mass moment of inertia Jo at the other end (see Figure below). Propeller; mass m, mass moment of inertia J d Data: d = n, cm, l = n2 m, m = 20*n3 kg, Jo = 2*n4 kgm?. Numbers n1, n2, n3, n4 are given in file "A1T1_Numbers.pdf" (see Task 1). Task 2.1 - Determine the fundamental natural frequency of vibration of the shaft in axial vibration. [5%] Task 2.2 - Determine the fundamental natural frequency of vibration of the shaft in torsional vibration. [10%] Task 2.3 - Is it possible to change the system parameters (d, 1, m, Jo) such that the fundamental frequencies for both axial and torsional vibration become identical? [10%] If yes, what are the new parameter values? Explain the method and report your detailed analysis leading to the new values. • If no, explain in detail why it is impossible. Note 1: In Tasks 2.1 and 2.2, derive boundary conditions, start from the relevant equation of motion and apply the boundary conditions, find characteristic equation, solve it for natural frequencies, and find the fundamental frequency. Note 2: In Tasks 2.1 and 2.2, state and justify ALL assumptions made. A steel shaft of diameter d and length I is fixed at one end and carries a propeller of mass m and mass moment of inertia Jo at the other end (see Figure below). Propeller; mass m, mass moment of inertia J d Data: d = n, cm, l = n2 m, m = 20*n3 kg, Jo = 2*n4 kgm?. Numbers n1, n2, n3, n4 are given in file "A1T1_Numbers.pdf" (see Task 1). Task 2.1 - Determine the fundamental natural frequency of vibration of the shaft in axial vibration. [5%] Task 2.2 - Determine the fundamental natural frequency of vibration of the shaft in torsional vibration. [10%] Task 2.3 - Is it possible to change the system parameters (d, 1, m, Jo) such that the fundamental frequencies for both axial and torsional vibration become identical? [10%] If yes, what are the new parameter values? Explain the method and report your detailed analysis leading to the new values. • If no, explain in detail why it is impossible. Note 1: In Tasks 2.1 and 2.2, derive boundary conditions, start from the relevant equation of motion and apply the boundary conditions, find characteristic equation, solve it for natural frequencies, and find the fundamental frequency. Note 2: In Tasks 2.1 and 2.2, state and justify ALL assumptions made.

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