A water turbine of inertia ?=500 kg.m2 is mounted on a two steel shafts as shown in Fig. 2.If each steel shaft is modelled as torsional spring while ??? represent the torsional springconstant of the i-shaft where ??1=100 N.m/rad and ??2=200 N.m/rad. Furthermore, ??1 ̇indicates as an external moment acting on the turbine and the output of this system is ?.a) Derive the equation of motion for the system and find the state space representation.b) Study the internal stability for the system.c) Study the BIBO stability for the system.d) Calculate the normalized eigenvectors for the system. A water turbine of inertia J=500 kg.m² is mounted on a two steel shafts as shown in Fig. 2.If each steel shaft is modelled as torsional spring while Kti represent the torsional springconstant of the i-shaft where kt₁=100 N.m/rad and kt2=200 N.m/rad. Furthermore, Mt1indicates as an external moment acting on the turbine and the output of this system is .M₁10₁K₁2k₁Turbine (₂)Fig. 2a) Derive the equation of motion for the system and find the state space representation.b) Study the internal stability for the system.c) Study the BIBO stability for the system.d) Calculate the normalized eigenvectors for the system.

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Answered: A water turbine of inertia ?=500 kg.m2…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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A water turbine of inertia ?=500 kg.m2 is mounted on a two steel shafts as shown in Fig. 2.
If each steel shaft is modelled as torsional spring while ??? represent the torsional spring
constant of the i-shaft where ??1=100 N.m/rad and ??2=200 N.m/rad. Furthermore, ??1 ̇
indicates as an external moment acting on the turbine and the output of this system is ?.

a) Derive the equation of motion for the system and find the state space representation.
b) Study the internal stability for the system.
c) Study the BIBO stability for the system.
d) Calculate the normalized eigenvectors for the system.

A water turbine of inertia J=500 kg.m² is mounted on a two steel shafts as shown in Fig. 2.
If each steel shaft is modelled as torsional spring while Kti represent the torsional spring
constant of the i-shaft where kt₁=100 N.m/rad and kt2=200 N.m/rad. Furthermore, Mt1
indicates as an external moment acting on the turbine and the output of this system is .
M₁1
0₁
K₁2
k₁
Turbine (₂)
Fig. 2
a) Derive the equation of motion for the system and find the state space representation.
b) Study the internal stability for the system.
c) Study the BIBO stability for the system.
d) Calculate the normalized eigenvectors for the system.

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