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MDOF Free Vibration

MDOF Free Vibration - CE 573 Structural Dynamics Example...

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CE 573: Structural Dynamics Example: Solving the Free Vibration Problem Given: A three-story building is modeled as shown. The dead load per unit length for each horizontal girder varies with each floor; you may assume that the weight of each column is negligible in comparison. Use E = 29,000 ksi and for all columns, and assume that the horizontal girders are rigid. The building is given the following initial displacement and initial velocity: 4 600 in I = { } { } 1.5 ft 0 ( 0) 2.7 ft ; ( 0) 0 . 4.4 ft 10 ft/sec u t u t = = = = ± Required: Determine the free vibration response of this building. Solution: 1. Property matrices, natural frequencies, mode shapes, and modal matrices – from the previous example: [ ] [ ] 2 kip-sec kip in in 0.04141 0 0 299.29 209.78 0 0 0.03882 0 , 209.78 258.97 49.189 0 0 0.02588 0 49.189 49.189 M K = = { } { } { } { } { } { } rad 1 sec 1 rad 2 sec 2 rad 3 sec 3 25.08 ; 0.3927 0.5115 0.7643 .
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  • Fall '05
  • Whalen
  • free vibration, Mode shape, Structural Dynamics Example, Free Vibration Problem, following initial displacement

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