Full exam for Mechanical Systems Dynamics in the Mechanical Engineering degree programme at Politecnico di Milano. The document covers: Mechanical System Dynamics - Proff. Bruni, Corradi 14 September 2015 The naval crane reported in figure is made of steel beams with the following properties: beams AE, BD, DE and DF m = 10 kg/m, EJ = 5.0e6 Nm2, EA = 2.6e8 N all other beams m = 50 kg/m, EJ = 1.0e8 Nm2, EA
Full exam for Mechanical Systems Dynamics in the Mechanical Engineering degree programme at Politecnico di Milano. The document covers: Mechanical System Dynamics - Proff. Bruni, Corradi 14 September 2015 The naval crane reported in figure is made of steel beams with the following properties: beams AE, BD, DE and DF m = 10 kg/m, EJ = 5.0e6 Nm2, EA = 2.6e8 N all other beams m = 50 kg/m, EJ = 1.0e8 Nm2, EA
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Mechanical System Dynamics - Proff. Bruni, Corradi 14 September 2015 The naval crane reported in figure is made of steel beams with the following properties: beams AE, BD, DE and DF m = 10 kg/m, EJ = 5.0e6 Nm2, EA = 2.6e8 N all other beams m = 50 kg/m, EJ = 1.0e8 Nm2, EA = 1.3e9 N (Assume the beam sections AC and BD to be made of four equal portions) 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 analysi ng its response in the 0 -20Hz frequency range (consider a safety factor of 1.5). 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. Assign the values of and so that they result in the following damping ratios for the first and the fourth vibration modes: 1=2%, 4=1% (report the computed values of and in the table at the back of this paper). Then calculate the structure frequency response function which relates the input force in node B to the output horizontal velocity evaluated in node B and the vertical acceleration evaluated in the node G (assume F to vary in the frequency range 0 -20Hz). Plot the magnitude and phase diagrams and save the Matlab figure s in the 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 same two frequency response functions specified in…
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