Vibration question; P-1 Q-9 R-0 S-1 T-0 U-5
Posted: Tue Apr 26, 2022 3:57 pm
Vibration question;
P-1
Q-9
R-0
S-1
T-0
U-5
Figure Q1 (a) shows a left wing of an aircraft V-22 OSPREY carrying a single propeller engine with a mass, m = 2P00 kg. The wing has a length, L = 1000 mm and is made of aluminium 7005 alloy with the Young's modulus, E = 7R GPa. The whole concept of the left wing with a propeller engine can be simplified as a cantilever beam with a mass on its end as shown in Figure Q1 (b). The beam has a rectangular cross section with the height, h = 180 mm and width, b = 5T0 mm. The propeller engine produced an upward force which expresses in a function of F(t) = 2000 cos 35t. =
(a) Construct the equivalent spring-mass system of the left wing based on Figure Q1(b) by including the direction of vibration motion. (2 marks) (b) Sketch the free-body diagram of the system of the left wing based on the equivalent spring-mass system in question Q1(a). (2 marks) Develop the equation of motion of the system on the left wing. (2 marks) (d) Determine the maximum amplitude of vibration of the left wing caused by an upward force produced by the propeller engine. (4 marks) (e) Justify whether the resonance will occur or not to the system? (4 marks) (f) By using appropriate solution of the vibration response, analyze the deflection of the left wing at time, t = 1 s and t = 70 s. Use initial displacement, Xo = 0.1 mm and initial velocity, xo = 1.0 m/s. Please conclude briefly what would happen to the left wing based on the comparison of vibration response at t=1s and t = 70 s. (11 marks)
- Vibration Question P 1 Q 9 R 0 S 1 T 0 U 5 1 (64.08 KiB) Viewed 27 times
Q-9
R-0
S-1
T-0
U-5
- Vibration Question P 1 Q 9 R 0 S 1 T 0 U 5 2 (106.04 KiB) Viewed 27 times
(a) Construct the equivalent spring-mass system of the left wing based on Figure Q1(b) by including the direction of vibration motion. (2 marks) (b) Sketch the free-body diagram of the system of the left wing based on the equivalent spring-mass system in question Q1(a). (2 marks) Develop the equation of motion of the system on the left wing. (2 marks) (d) Determine the maximum amplitude of vibration of the left wing caused by an upward force produced by the propeller engine. (4 marks) (e) Justify whether the resonance will occur or not to the system? (4 marks) (f) By using appropriate solution of the vibration response, analyze the deflection of the left wing at time, t = 1 s and t = 70 s. Use initial displacement, Xo = 0.1 mm and initial velocity, xo = 1.0 m/s. Please conclude briefly what would happen to the left wing based on the comparison of vibration response at t=1s and t = 70 s. (11 marks)