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Mechanical System Dynamics - Proff. Bruni, Corradi June 22nd 2015 Fig.1 Consider the cantilever truss shown in Fig.1. A lumped mass is attached in A (mass M=1000 kg, moment of inertia I=60 kgm 2). All beams are made of steel (E=2.06e11 N/m2, =7800 kg/m3) and have IPE200 cross section (A=2.848e-3 m2, J=1.9432e-5 m4). Damping is defined according to the “proportional damping” assumption: [C]=[M]+[K], with =0.4 s-1 and =6.0e-5 s. 1. Define a FE model of the structure in the 0-15 Hz frequency range . Sa ve 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 matrices and the corresponding natural frequencies and 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 modal mass, modal damping and modal stiffness parameters for the first two vibration modes , consider ing the standard Matlab eigenvector scaling (the 2 -norm of the eigenvector is set to 1). 4. Calculate the structure frequency response functions which relate the input force in node A (perpendicular to the axis of the beam connecting points A and B) to the output vertical displacements evaluated in nodes A and B (assume the inpu t force to vary in the 0 -15 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). 5. Calculate the same two frequency…