Identification of the dynamic characteristics of nonlinear structures

 
 
s = l
(7-22)
where [m,] and 
are the 
element mass and stiffness matrices which have been
appropriately expanded to the global dimension of the system, 
is the total number of

---

7
Possibilities and Limitations of Analytical Model Improvement
2 3 7
elements and, 
and am the design variable changes associated with the 
element.
With [AM] and [AK] being expressed as 
the eigensensitivity coefficients
 
 
 
and 
can be obtained using the analytical model (see Appendix II).
Based on the first order sensitivity analysis, the following relationship between the the
changes of modal parameters and the changes of physical parameters can be established:
 
(7-23)
where m experimental modes are supposed to have been measured. Again, the measured
coordinates are assumed to be incomplete, i.e. 
where 
When a
sufficient number m of modes are measured, (7-23) becomes overdetermined and the
SVD technique can be used to solve for and
iteratively.
To assess the practical applicability of the Inverse Eigensensitivity Analysis method, the
fixed-free GARTEUR structure shown in Fig.7.20 was investigated. Only stiffness
errors are introduced by overestimating the 
(nodes 
and 
(nodes 14-
16), 
(nodes 29-30) and 
and 
(nodes 62, 14, 63) element stiffness matrices
by 100% (figure 7.21). The hatched nodes shown in Fig.7.21 with their translational
degrees of freedom 
are supposed to be measured. According to 
the
minimum number of modes required to update the analytical model is 
(where 
is the total number and so the total number of design
variables according to (7-22) when stiffness modelling errors are considered and 
is
the number of measured coordinates (2 translational degrees at 36 nodes)). During the
calculation, the first 4 modes are supposed to have been measured (twice as many as the
minimum number required). The exact stiffness error matrix is shown in Fig.7.22 and
the iteration results are shown in 

---