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Mechanical System Dynamics - Proff. Bruni, Corradi 21 July 2015 The welded plane frame in the figure above is entirely made of circular pipes . All pipes have the same properties: m=110 kg/m, EA=2 .8E9 N, EJ=3.0 E7 Nm 2. The geometry data are as follows : L1=6.4 m, L 2=4 m, L3=2 m, H1=6m, H 2=0.8 m, H 3=3m. Damping is defined according to the proportional damping assumption: [C]=[M]+[K], with =0.3 s-1 and =5.0e-5 s. 1. Define a FE model of the structure suitable for analysing its response in the 0 -80Hz 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 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. Calculate the structure frequency response functions which relate the input force (a vertical force applied in node A) to the output vertical velocity of node B and to the output horizontal velocity of node C (assume the input force to vary in the 0-80Hz frequency range and set the frequency resolution to 0. 1Hz). 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. Calculate the amplitude of the vertical acceleration of node B which is produced by an unbalanced mass mu=100kg located in A and rotating at 1200 rpm around an axis perpendicular to the plane of the drawing. Also compute the same acceleration in case of doubling…