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Mechanical System Dynamics - Proff. Bruni, Corradi 4 September 2015 m [kg/m] EA [N] EJ [Nm2] Principal beams 4 4E07 4E03 Reinforcement beams 1 1E05 1E3 The structure in figure is made of beams with the properties specified in the table above. 1. Define a FE model of the structure suitable for analysing its response in the 0 -20Hz frequency range (consider 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 i s 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 structure vibration modes. Save the images of the first 3 mode shapes in 3 distinct .fig files (named FNxxx2.fig, FNxxx3.fig, FNxxx4.fig), with the indication of the associated natural frequencies. 3. Assign the values of  and  so that they result in the following damping ratios for the first two vibration modes: 1=2%, 2=3% (report the computed values of  and  in the table at the back of this paper) . Then c alculate the struct ure frequency response function which relat es the input force in node k to the output vertical displacement evaluated in node j (assume Fk to vary in the frequency range 0 -20Hz). Plot the magnitude and phase diagrams and save the Matlab figure in a file FNxxx5.fig. Provide a short comment to the diagrams (in the table at the back of this paper). 4. Compute the constraint vertical force in point C which results from a periodic vertical force applied in node k consisting in the superposition of two harmonic components: 1=3Hz (A1=500N, Ψ 1=0deg) and 2=4Hz (A2=500N, Ψ2=45deg). Plot the time history (10 s) of the computed steady state vertical force and save the Matlab figure in a file FNxxx6.fig.…