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AN ALTERNATIVE METHOD FOR INTRODUCING UNCERTAINTIES IN THE FLEXIBLE MODEL
An alternative method to the approach of chapter 3 (section 4.) is presented for introducing uncertainties in the frequency of the bending modes. Let ші and & the natural frequency and damping ratio of the ith flexible mode. When reducing the real modal state-space representation to this single mode, one obtains :
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An uncertainty in the natural frequency ші is introduced as:
— (1 + Si)u>oi (4-12)
where u>oi denotes the nominal value and Si the associated relative variation. Assuming that the damping ratio and frequency variation are
small (i. e. £; <£. 1 and |<5*| 1), the dynamic matrix can then be ap
proximated as follows:
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Ai can thus be rewritten as A* = Аоі + ДА; with : ,2 |
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—2£ja>oi — (1 + 2<5;)a>o;2
1 0
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ДА; is a rank one matrix, which is factorized under the form ДА; = —MiSiNi. The uncertainty can hence be expressed as a feedback of gain Si between the scalar fictitious input e/ and output z/ :
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A possible choice for M; and iV; is :
