25 The connection of coal mining trolleys by couplings of stiffness in function of the modulus, E of the coupler as show

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25 The Connection Of Coal Mining Trolleys By Couplings Of Stiffness In Function Of The Modulus E Of The Coupler As Show 1 (245.58 KiB) Viewed 36 times

25 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⎣⎡​100​010​001​⎦⎤​⎣⎡​x¨1​x¨2​x¨3​​⎦⎤​+l3EI​⎣⎡​3−30​−36−3​0−33​⎦⎤​⎣⎡​x1​x2​x3​​⎦⎤​=⎣⎡​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)