CE573_Homework11_2010 - CE 573 Structural Dynamics Homework...

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CE 573 – Structural Dynamics Homework #11 due 29 November 2010, Monday, 1:30pm 1) For the 2-story building with fixed foundation conditions as shown below: a. Determine the natural vibration frequencies and modes; express the frequencies in terms of m , E I , and h . b. Verify that the modeshapes satisfy the orthogonality properties. c. Normalize each mode so that the roof displacement is unity. Sketch the modeshapes and identify the associated natural frequencies. d. Normalize each mode so that the modal mass matrix is a unity (identity) matrix, i.e. find the mass- normalized modeshapes. e. Consider the following two cases: i. a constant force F o is applied at first floor level quasi-statically to give an initial displaced shape, and the force is removed to start free-vibration response; ii. a constant force F o is applied at second floor level quasi-statically to give an initial displaced shape, and the force is removed to start free-vibration response. In which case the relative contribution of the first mode to the total response is greater?
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This note was uploaded on 02/03/2011 for the course CE 573 taught by Professor Various during the Spring '11 term at American University of Science & Tech.

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