3. A vehicle is modelled as a large rectangular mass with centre of gravity located at G, see Figure 3. It is given a sm

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3 A Vehicle Is Modelled As A Large Rectangular Mass With Centre Of Gravity Located At G See Figure 3 It Is Given A Sm 1 (45.18 KiB) Viewed 30 times

3. A vehicle is modelled as a large rectangular mass with centre of gravity located at G, see Figure 3. It is given a small downwards vertical displacement and a small angular cew rotation and released. The mass starts to vibrate. The objective is to determine the natural frequencies of vibration. te L₁ Figure 3: This Figure refers to Question 3 (a) Assuming just two forces act - one at the front F, and one at the rear F, (both due to the suspension), sketch a free body diagram for the system assuming the small displacements z and as described above. (b) Write down the equations of motion for the geometrically exact case (taking moments about G). Then linearise those equations and express them in matrix form MX + KX = 0, where M is the inertia matrix, K is the stiffness matrix and X is the position vector. (c) Assume the following: Mass m = 1200 kg. • Radius of gyration rc = 0.75 m. • Front wheel suspension stiffness k = 20 kN/m. • Rear wheel suspension stiffness k, = 25 kN/m. • Distances to centre of mass G: L₁ = 1m and L₂ = 1.5m. Determine the natural frequencies. (Total Q3: 20 marks) [3 marks] [10 marks] [7 marks]