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Mechanical System Dynamics - Proff. Bruni, Corradi July 10th 2015 The figure above shows a beam model of a suspended bridge tower. Consider the tower as not being attached to the rest of the bridge (this is actually happening during the erection stage). All lengths in the drawing are in m. The beam properties are: Legs: m=6600 kg/m; EA=1.6E11 N; EJ=1.0E13 Nm2; Transverse beams: m=12000 kg/m; EA=3.6E11 N; EJ=1.2E12 Nm2. Structural damping is defined according to [C]=[M]+[K], with =0.2 s-1 and =2.0e-4 s. 1. Define a FE model of the structure in the 0-5 Hz frequency range (use a safety factor of 2.0) . Save the image of the undeformed structure in a .fig file, named FNxxx1.fig (F is the first letter of your family name, N is the first letter of your name, xxx are the last three digits of your matriculation number; e.g. Bruni Stefano 123456: BS456). 2. Calculate the three lowest natural frequencies of the system and the corresponding mode shapes. Save the images of these 3 mode shapes in 3 distinct .fig files (named FNxxx2.fig, FNxxx3.fig, FNxxx4.fig), with the indication of the associated natural frequencies. 3. Compute the structure frequency response functions which relat e the input force F at node A to the output horizontal acceleration of the tower evaluated at nodes A and B (note that B is located at an height of 1 90m). Assume the input force F to vary in the 0-5 Hz frequency range and set the frequency resolution to 0.01 Hz. Plot the magnitude and phase diagrams and save the Matlab figures in two files FNxxx5.fig and FNxxx6.fig. Provide a short comment to the diagrams (in the table at the back of this paper). 4. Compute the structure frequency response function s which re late the input horizontal displacement applied in phase at both bases of the tower to the…