Figure Q2 shows the schematic diagram of wind turbine which used in power plant. By using the exact solution method, it is found that the fundamental natural frequency for the system is wn = 0.6/kt/J rad/s. Assume that J1 =J2= J, and k1 = k2 = kr-

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Vibration subject.

For question 2 (b) , the value of X = 1

Q2 Figure Q2 shows the schematic diagram of wind turbine which used in power plant.
By using the exact solution method, it is found that the fundamental natural frequency
for the system is wn = 0.6/k;/J rad/s. Assume that J, =J; = J, and k;1 = k2 = k.
(a) Establish the free body diagram and equation of motion in the matrix form for
gear box, generator, low-speed shaft and high-speed shaft.
(b) By using standard matrix iteration approximation method, determine the lowest
natural frequency in Hertz unit and its corresponding mode shape for Q2(a)
0.1
answer if the initial trial vector is (). Use J= 2, and k, = X, and show up
2.9
to four (4) iterations calculation. Here, the value of X indicating of the number
of your group.
For example, if your group number is 15 gives the value of k, = 15. If your
group number is 9 gives the value of k; = 9.
(c)
By using Rayleigh's method, predict the fundamental natural frequency in Hertz
unit for Q2(a) answer. Use the same initial trial vector in Q2(b).
(d)
Please justify which approximate method from Q2(b) and Q2(c) is more
accurate.
Transcribed Image Text:Q2 Figure Q2 shows the schematic diagram of wind turbine which used in power plant. By using the exact solution method, it is found that the fundamental natural frequency for the system is wn = 0.6/k;/J rad/s. Assume that J, =J; = J, and k;1 = k2 = k. (a) Establish the free body diagram and equation of motion in the matrix form for gear box, generator, low-speed shaft and high-speed shaft. (b) By using standard matrix iteration approximation method, determine the lowest natural frequency in Hertz unit and its corresponding mode shape for Q2(a) 0.1 answer if the initial trial vector is (). Use J= 2, and k, = X, and show up 2.9 to four (4) iterations calculation. Here, the value of X indicating of the number of your group. For example, if your group number is 15 gives the value of k, = 15. If your group number is 9 gives the value of k; = 9. (c) By using Rayleigh's method, predict the fundamental natural frequency in Hertz unit for Q2(a) answer. Use the same initial trial vector in Q2(b). (d) Please justify which approximate method from Q2(b) and Q2(c) is more accurate.
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