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 :

AN ALTERNATIVE METHOD FOR INTRODUCING UNCERTAINTIES IN THE FLEXIBLE MODEL

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:

Ai can thus be rewritten as A* = Аоі + ДА; with :

,2

Подпись: (4.13)

Подпись: AQ; = Подпись: 1 Подпись: 0 Подпись: and ДА, = Подпись: 0 0 Подпись: 26iWoi2 1 0 Подпись: (4.14)

—2£ja>oi — (1 + 2<5;)a>o;2
1 0

AN ALTERNATIVE METHOD FOR INTRODUCING UNCERTAINTIES IN THE FLEXIBLE MODEL

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/ :

AN ALTERNATIVE METHOD FOR INTRODUCING UNCERTAINTIES IN THE FLEXIBLE MODEL

A possible choice for M; and iV; is :

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