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a left wing carrying single propeller engine with a mass, m= 2P00 kg. The wing has a length, L = 1Q00 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 = 1S0 mm and width, b = 5T0 mm. The propeller engine produced an upward force which expresses in a function of F(t) = 2U00 cos 35t. Note: The values of P, Q, R, S, T, and U depend on the respective 1st, 2nd, 3rd, 4th, 5th and 6th digit of your FIRST GROUP MEMBER’S matric number as the following number format AD PQRSTU. For example, if the first group member's matric number is AD 170154 gives the value P = 1, Q = 7, R = 0, S = 1, T = 5 and U = 4, thus mass, m = 2100 kg, length, L = 1700 mm, Young's modulus, E = 70 GPa, height, h = 110 mm, width, b = 550 mm and F(f) = 2400 cos 35t. Construct the equivalent spring-mass system of the left wing based on Figure Q1(b) by including the direction of vibration motion. (a) (b) Sketch the free-body diagram of the system of the left wing based on the equivalent spring-mass system in question Q1(a). (c) Develop the equation of motion of the system on the left wing. (d) Determine the maximum amplitude of vibration of the left wing caused by an upward force produced by the propeller engine. (е) Justify whether the resonance will occur or not to the system?

a left wing carrying single propeller engine with a mass, m= 2P00 kg. The wing has a length, L = 1Q00 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 = 1S0 mm and width, b = 5T0 mm. The propeller engine produced an upward force which expresses in a function of F(t) = 2U00 cos 35t. Note: The values of P, Q, R, S, T, and U depend on the respective 1st, 2nd, 3rd, 4th, 5th and 6th digit of your FIRST GROUP MEMBER’S matric number as the following number format AD PQRSTU. For example, if the first group member's matric number is AD 170154 gives the value P = 1, Q = 7, R = 0, S = 1, T = 5 and U = 4, thus mass, m = 2100 kg, length, L = 1700 mm, Young's modulus, E = 70 GPa, height, h = 110 mm, width, b = 550 mm and F(f) = 2400 cos 35t. Construct the equivalent spring-mass system of the left wing based on Figure Q1(b) by including the direction of vibration motion. (a) (b) Sketch the free-body diagram of the system of the left wing based on the equivalent spring-mass system in question Q1(a). (c) Develop the equation of motion of the system on the left wing. (d) Determine the maximum amplitude of vibration of the left wing caused by an upward force produced by the propeller engine. (е) Justify whether the resonance will occur or not to the system?

Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter5: Stresses In Beams (basic Topics)
Section: Chapter Questions
Problem 5.5.28P: A foot bridge on a hiking trail is constructed using two timber logs each having a diameter d = 0.5...
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pls use this number as values 200201

Figure Q1(a)
Transcribed Image Text:Figure Q1(a)
Q1 Figure Q (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 = 1Q00 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 = 150 mm and width, b = 5TO mm. The propeller engine produced an upward force which expresses in a function of F(f) = 2U00 cos 35t. Note: The values of P, Q, R, S, T, and U depend on the respective 1st, 2nd, 3rd, 4th, 5th, and 6th digit of your FIRST GROUP MEMBER'S matric number as the following number format AD PQRSTU. For example, if the first group member's matric number is AD 170154 gives the value P = 1, Q = 7, R = 0, S = 1, T = 5 and U = 4, thus mass, m = 2100 kg, length, L = 1700 mm, Young's modulus, E = 70 GPa, height, h = 110 mm, width, b = 550 mm and F(f) = 2400 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. (b) Sketch the free-body diagram of the system of the left wing based on the equivalent spring-mass system in question Q1(a). (c) Develop the equation of motion of the system on the left wing. (d) Determine the maximum amplitude of vibration of the left wing caused by an upward force produced by the propeller engine. (e) Justify whether the resonance will occur or not to the system?
Transcribed Image Text:Q1 Figure Q (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 = 1Q00 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 = 150 mm and width, b = 5TO mm. The propeller engine produced an upward force which expresses in a function of F(f) = 2U00 cos 35t. Note: The values of P, Q, R, S, T, and U depend on the respective 1st, 2nd, 3rd, 4th, 5th, and 6th digit of your FIRST GROUP MEMBER'S matric number as the following number format AD PQRSTU. For example, if the first group member's matric number is AD 170154 gives the value P = 1, Q = 7, R = 0, S = 1, T = 5 and U = 4, thus mass, m = 2100 kg, length, L = 1700 mm, Young's modulus, E = 70 GPa, height, h = 110 mm, width, b = 550 mm and F(f) = 2400 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. (b) Sketch the free-body diagram of the system of the left wing based on the equivalent spring-mass system in question Q1(a). (c) Develop the equation of motion of the system on the left wing. (d) Determine the maximum amplitude of vibration of the left wing caused by an upward force produced by the propeller engine. (e) Justify whether the resonance will occur or not to the system?
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