Identification of the dynamic characteristics of nonlinear structures

 
+ 
 
 + 
 J
i = l
i = l
(7-17)
where and 
are the first- and second-order sensitivity coefficients. Suppose n out of
N coordinates have been measured for the 
mode then, based on 
to a first order
approximation, we have:
(7-18)
where 
is the sensitivity matrix for n measured coordinates and one measured
eigenvalue of the 
mode, and can be calculated in a way as illustrated in Appendix II of
this thesis, and 
is the difference vector between the measured and analytical
eigenvector and eigenvalue of the 
mode. If m measured modes are available, (7-18a)
can be rewritten as
m(n+l)xL 
(7-19)
When m(n+l) L, (7-19) becomes a set of 
linear algebraic equations and
the SVD technique can be used to solve 
Since (7-19) is formulated based on 
order approximation, the exact solution of 
cannot be obtained directly and an iterative
procedure has to be introduced as illustrated in Fig.7.16. Again, after (P) has been
calculated, the updated model can be reconstructed using the the analytical model.

---

 Possibilities and Limitations of Analytical 
Improvement
2 2 9
measured incomplete data,
I,,
complete analytical model
,
calculate the eigensensitivity matrix [S] based on
Appendix and the 
vector between
measured and analytical modal parameters
solve the linear algebraic equations [S] (P} = 
for (P) and update the analytical mass and stiffness
matrices using the calculated 
NO
solve the eigenvalue problem of the updated system
updated/improved
analytical model
Updating Process Using Inverse Eigensensitivity Analysis

---

7
Possibilities and Limitations of Analytical Model Improvement
2 3 0