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Higher Mode Inverse Iteration

Higher Mode Inverse Iteration - CE 573 Structural Dynamics...

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CE 573: Structural Dynamics Example: Inverse Vector Iteration for Higher Modes Given: A six-story building is modeled as shown. Parameters are , psi, and . 2 66 lb-sec /in m = 6 30 10 E = × 4 882 in I = Required: Use inverse vector iteration to find the natural frequency and mode shape for mode #2, assuming that the mode shape for modes #1 is known. Solution: 1. Property matrices – from previous example: [ ] [ ] 2 3 lb-sec lb in in 66 217.78 108.89 66 108.89 217.78 108.89 66 108.89 217.78 108.89 ; 1 66 108.89 217.78 108.89 66 108.89 217.78 108.89 66 108.89 108.89 M K = = 0 × Must also have the first mode shape. In the example on Rayleigh’s Quotient, we saw that the static displacement due to self-weight – { } [ ] [ ] { } 1 static K M g φ = – gave a very good estimate of mode #1’s natural frequency. Let’s use regular inverse iteration to improve this estimate: >> mmat = diag([66 66 66 66 66 66]) mmat = 66 0 0 0 0 0 0 66 0 0 0 0 0 0 66 0 0 0
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