CE573_Solution_Homework10_2010

CE573_Solution_Homework10_2010 - 1 CE573 – Structural...

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Unformatted text preview: 1 CE573 – Structural Dynamics Homework #10 1. 2 3 4 5 There is another approach to illustrate the forces acting on this system. In this second approach -- called the D’Alembert’s approach—t he inertial forces (tangential and centrifugal) are shown on the figure. They are shown as acting in the direction opposite to associated accelerations. and the rest follows just as done above. 6 2. Using the interstory drifts as the coordinates, say 1 ∆ and 2 ∆ , the equations of motion for free vibration can be written as (remember the free-body diagrams and force balances we did in class): 1 1 2 2 2 story story k M M M M k     ∆   ∆     + =           ∆ ∆             ɺɺ ɺɺ ɺɺ ɺɺ ɺɺ ɺɺ ɺɺ ɺɺ Casting the problem of finding modal frequencies and modeshapes as an eigenvalue problem, the modal frequencies 1 ϖ and 2 ϖ will be those unique frequencies that will satisfy the characteristic equation, i.e. will be those unique frequencies that will satisfy the characteristic equation, i....
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CE573_Solution_Homework10_2010 - 1 CE573 – Structural...

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