A turbine rotor is mounted on a stepped shaft that is fixed at both ends as shown inThe torsional stiffnesses of the two segments of the shaft are given by ka = 3,000 N-m/radand k2 = 4,000 N-m/rad. The turbine generates a harmonic torque given by M(t) = Mo coswt about the shaft axis with M, = 200 N-m and w = 500 rads. The mass moment of inertiaof the rotor about the shaft axis is Jo = 0.05 kg-m. Assuming the equivalent torsionaldamping constant of the system as c, = 2.5 N-m-s/rad, determine the steady-state responseof the rotor, 6(1).O(1)keM(1) = M, cos otTurbine rotor, Jo

Transient response: the response of the system due to free vibration is called the transient…

A turbine rotor is mounted on a stepped shaft that is fixed at both ends as shown in The torsional stiffnesses of the two segments of the shaft are given by k = 3,000 N-m/rad and k2 = 4,000 N-m/rad. The turbine generates a hamonic torque given by M(t) = Mo cos ot about the shaft axis with Mo = 200 N-m and w = 500 rad/s. The mass moment of inertia of the rotor about the shaft axis is J = 0.05 kg-m. Assuming the equivalent torsional damping constant of the system as c, = 2.5 N-m-s/rad, determine the steady-state response of the rotor, 6(1). M(1) - Mo cos ot Turbine rotor, Jo

A turbine rotor is mounted on a stepped shaft that is fixed at both ends as shown in The torsional stiffnesses of the two segments of the shaft are given by k = 3,000 N-m/rad and k2 = 4,000 N-m/rad. The turbine generates a hamonic torque given by M(t) = Mo cos ot about the shaft axis with Mo = 200 N-m and w = 500 rad/s. The mass moment of inertia of the rotor about the shaft axis is J = 0.05 kg-m. Assuming the equivalent torsional damping constant of the system as c, = 2.5 N-m-s/rad, determine the steady-state response of the rotor, 6(1). M(1) - Mo cos ot Turbine rotor, Jo

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

A turbine rotor is mounted on a stepped shaft that is fixed at both ends as shown in
The torsional stiffnesses of the two segments of the shaft are given by ka = 3,000 N-m/rad
and k2 = 4,000 N-m/rad. The turbine generates a harmonic torque given by M(t) = Mo cos
wt about the shaft axis with M, = 200 N-m and w = 500 rads. The mass moment of inertia
of the rotor about the shaft axis is Jo = 0.05 kg-m. Assuming the equivalent torsional
damping constant of the system as c, = 2.5 N-m-s/rad, determine the steady-state response
of the rotor, 6(1).
O(1)
ke
M(1) = M, cos ot
Turbine rotor, Jo

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