Consider a disc-shaft assembly shown as below. Initially, a torque is applied to the disc and...

 

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Consider a disc-shaft assembly shown as below. Initially, a torque is applied to the disc and suddenly it is released. The torsional oscillation occurs during the dynamic movement and the amplitude decrement for the sequential cycles are observed to happen 40% of the initial value. Assume that polar moment of inertia of the disc is J-0.06 kg-m², shear modulus of the shaft is G-45 GPa, diameter of the shaft d=100 mm, 1=500 mm. The torsional stiffness of the shaft is given by k₁=G*I/L. Assume that shaft have negligible mass. Answer the following questions: a) Show the SDOF lumped parameter of the system. Label the torsional displacement as 0. b) What is the logarithmic decrement? c) What is the damping ratio? d) What is the viscous coefficient, c? e) What is the natural frequency? f) What is the damped time period, Ta? l d I DISC SHAFT kt Consider a disc-shaft assembly shown as below. Initially, a torque is applied to the disc and suddenly it is released. The torsional oscillation occurs during the dynamic movement and the amplitude decrement for the sequential cycles are observed to happen 40% of the initial value. Assume that polar moment of inertia of the disc is J-0.06 kg-m², shear modulus of the shaft is G-45 GPa, diameter of the shaft d=100 mm, 1=500 mm. The torsional stiffness of the shaft is given by k₁=G*I/L. Assume that shaft have negligible mass. Answer the following questions: a) Show the SDOF lumped parameter of the system. Label the torsional displacement as 0. b) What is the logarithmic decrement? c) What is the damping ratio? d) What is the viscous coefficient, c? e) What is the natural frequency? f) What is the damped time period, Ta? l d I DISC SHAFT kt

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SOLUTION a The SDOF lumped parameter of the system is as follows Mass Negligible since the mass of t... View the full answer