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Unformatted text preview: mode shapes. x z 60 1 z 20 20 20 3. A simply-supported aluminum beam (E = 10.0 Msi, = 0.1 lbs/in 3 ) has a rectangular cross section of 0.4 inches by 0.8 inches and is 36 inches long. The beam has a force [F(t) = (5.0 lbs) sin t ] applied at its center. CROSS-SECTION x z F(t) 0.4 36 0.8 (a) Determine the natural frequencies and the mode shapes for the first three modes. (b) Write out the normal equations of motion using the first three modes. (c) Using these modes, determine the general center deflection of the beam as well as the contribution of each mode to this overall response. (d) Plot the individual modal amplitude and the total amplitude versus forcing frequency . x...
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- Fall '02