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Mechanical System Dynamics - Proff. Bruni, Corradi 12 February 2016 m [kg/m] EA [N] EJ [Nm2] External beams 4 4E07 4E03 Internal beams 1 1E05 1E3 The structure in figure is made of beams with the properties specified in the table above. Damping is defined according to the proportional damping assumption: [C]=[M]+[K]. 1. Define a FE model of the structure and 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 structure vibration modes. Save the images of the first 4 mode shapes in 4 distinct .fig files (named FNxxx2.fig, FNxxx3.fig, FNxxx4.fig, FNxxx5.fig), with the indication of the associated natural frequencies. 3. Calculate the structure frequency response function which relates the input force at the node k to the output horizontal displacement j (assume the input force to vary in the 0-10 Hz frequency range and set the frequency resolution to 0. 01Hz). Plot the magnitude and phase diagrams and save the Matlab figures in two files FNxxx6.fig. Provide a short comment to the diagrams (in the table at the back of this paper). 4. Calculate the same frequency response function specified in item 3, by developing a model in modal coordinates, limited to the first two modes. Plot the magnitude and phase diagrams superimposed to those of item 3 and save the Matlab figure name FNxxx7.fig. Provide a short comment to the diagrams (in the table at the back of this paper). 5. Compute the modal mass and stiffness of the first two modes and reassign the values of  and  so that they result in the following damping ratios for the first two vibration modes: 1=2%,…