Inverse Iteration

Inverse Iteration - CE 573: Structural Dynamics Example:...

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CE 573: Structural Dynamics Example: Inverse Vector Iteration Given: A two-story building is modeled as a shear-frame structure. Parameters are kg and N/m. 3 35 10 m 6 17.5 10 k Required: Use inverse vector iteration to obtain estimates of the fundamental natural frequency 1 ω and mode shape { } 1 a for this building. Solution: 1. Property matrices – [] 3 3 20 7 0 1 0 0 kg. 02 07 0 1 0 m m m ⎡⎤ × == ⎢⎥ × ⎣⎦ 66 6 6 6 4 2 2 6*17.5 10 2*17.5 10 105 10 35 10 N/m = N/m 22 2*17.5 10 2*17.5 10 35 10 35 10 kk k k kk +− × − × × −× × × × 6 2. Inverse iteration – since the choice of the trial vector { } 1 x is completely arbitrary, I will choose {} 1 0.5 . 1.0 x = ⎩⎭ I will also choose a tolerance of on my eigenvalue convergence criterion; this should give me about 3 digits of accuracy in my estimated mode shape. Using Matlab to do the computations, we iterate as follows: 6 10 >> mmat = diag([70*10^3 70*10^3]) mmat = 70000 0 0 70000 >> kmat = [105*10^6 -35*10^6; -35*10^6 35*10^6] kmat = 105000000 -35000000 -35000000 35000000 >> tolerance = 10^(-6); lambda1 = 1; x1 = [0.5; 1.0]
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This note was uploaded on 05/09/2008 for the course CE 573 taught by Professor Whalen during the Fall '05 term at Purdue.

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Inverse Iteration - CE 573: Structural Dynamics Example:...

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