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sensitivity based method for structural dynamic model improvement

sensitivity based method for structural dynamic model improvement

358 R. M. LIN ef al.(a)

358 R. M. LIN ef al.(a) estimated modifications of area S(b) estimated modifications of second moment of area IFig. 11. Estimated modifications of area S and moment of area I (first iteration/case 2).When m modes are measured, then (24) should bemodified to becomeCWPI{APP~ = {A

Structural dynamic model improvement 359Since (25a) is formulated based on first-order approximation, the exact solution of {Ap) cannot beobtained directly and an iterative procedure has to beintroduced as shown in Fig. 2. After {Ap} has beencalculated, the analytical model can be updated andthe sensitivity matrix [S] is reformulated. Such aprocess is repeated until the newly calculated (Ap]becomes sufficiently small in its Euclidean norm as isillustrated in Fig. 2.3.2. Frequency response function sensitivity methodFrequency response functions of a system willchange when its design variables change and the rateof such change is measured by sensitivity. Similar tothe case of eigenvalue and eigenvectors, based on theTaylor series representation, the relationship betweenthe change of frequency response function AaQ(w)and the vector of design variable changes {Ap} can beexpressed aswhere gi and w# are the first- and second-orderfrequency response function sensitivity coefficients.The first-order response function sensitivity coefficientsgi can be derived based on (21). Again,assume that n out of N coordinates of the ith columnof the receptance matrix {ax(w)>i have been measured(n < N) for a certain frequency range, then a firstorderapproximation, following linear algebraic(a) estimated modifications of area S(b) estimated modifications of second moment of area IFig. 12. Estimated modifications of area S and moment of area I (20th iteration/case 2).

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