Identification of the dynamic characteristics of nonlinear structures

LOCATION OF NONLINEARITY AND MODELLING ERRORS
IN ANALYTICAL MODEL IMPROVEMENT
So far, the nonlinearity location technique has been developed and has been verified
numerically as well as experimentally and it will be advantageous here to examine the
relationship between the two applications of (i) nonlinearity location and (ii) modelling
error location of a linear structure in the analytical model updating practice. The
discussion is made in this chapter for the location of modelling errors and will be referred
to from time to time in later chapters because of the mathematical similarity of nonlinearity
location and modelling error location. In modelling error location, [AK,.,] = 
and what
needs to be located are the dominant modelling errors in [AM] and [AK] (assume the
modelling errors are localised as they usually are in practice).
Following the same reasoning as that used for nonlinearity location, it can be seen that the
localised modelling errors in [AM] and [AK] can be located based on (5-4). Since in the
modelling error location case, 
therefore 
and (5-4) becomes
The modelling error location technique based on (5-25) has been reported in 
and we
will show here that it can be 
when measured FRF data are used.
Using measured FRF data, let 
 
 
 
 SO 
that (5-19) becomes
(5-26)
Again, it can be shown that when 
(5-26) will degenerate to (5-25). The location
technique given in (5-26) not only generalises the technique developed in 
but
because every measured FRF data point theoretically contains a contribution of all the

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 Location of Structural Nonlinearity
168
modes of the structure, the location of modelling errors becomes more consistent. This is
illustrated in Fig.527 based on the same mass-spring system used in the numerical case
studies of nonlinearity location. 
shows the exact stiffness modelling error
[AK], 
shows the error location results [AK] 
based on (5-25) and
shows the error location results