EG260 example_5 - EG-260 EG -260 Dynamics I - Example Sheet...

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EG-260 @Avril Slone 1 of 1 EG -260 Dynamics I - Example Sheet 5 Multi degree of freedom systems 1. Write down the equations of motions for the torsional system of two circular plates with moments of inertia I 1 and I 2 , and torsional stiffness k 1 and k 2 . Use variables θ 1 and θ 2 to describe the angular rotation of the two plates at any point in time. Determine the normal modes when I 1 = I 2 = I and k 1 = k 2 = k 2. Two equal masses are attached to a light string with tension T . Assuming T remains unchanged when the masses are displaced normal to the string, calculate normal mode frequencies of vibration. 3. Determine the natural frequencies and mode shapes of the system shown. 4. A two storey car park can be modelled as shown. Assuming
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