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5 The connection of coal mining trolleys by couplings of stiffness in function of the modulus, E of the coupler as shown
Posted: Thu Jul 14, 2022 2:52 pm
by answerhappygod
- 5 The Connection Of Coal Mining Trolleys By Couplings Of Stiffness In Function Of The Modulus E Of The Coupler As Shown 1 (39.7 KiB) Viewed 51 times
5 The connection of coal mining trolleys by couplings of stiffness in function of the modulus, E of the coupler as shown in Figure Q5 has induced a three degree of freedom vibration. The spring constant is known as, k=l3EI and the equation of motion for the system is given below: m⎣⎡100010001⎦⎤⎣⎡x¨1x¨2x¨3⎦⎤+l3EI⎣⎡3−30−36−30−33⎦⎤⎣⎡x1x2x3⎦⎤=⎣⎡000⎦⎤ (a) Draw the equivalent spring-mass model of the systems. (3 marks) (b) Determine the natural frequencies of the system. (8 marks) (c) Differentiate between the 1st ,2nd and 3rd vibration modes characteristics of the system based on the mode shape diagrams. Related data is tabulated in Table Q5. (14 marks)
Table Q5