Identification of the dynamic characteristics of nonlinear structures

 
=
[ x ( t )
(3-79)
Instead of taking the time domain average, let the averaging be done in the frequency
domain, Fourier transform both sides of 
then
 
=
 [ 
 
 
F * ( q )
 
 
(3-80)
With K,(o), which is the calculated first-order frequency response function based on (3-
70), to be available beforehand, 
can be derived based on equation (3-80) and
in this way, the computational efficiency can be improved.
3.6 
IDENTIFICATION OF NONLINEARITY
FREQUENCY RESPONSE FUNCTIONS
USING HIGHER-ORDER
So far, the theoretical basis of and measurement techniques for higher-order frequency
response functions have been discussed in some detail and the remaining question which
needs to be answered is: “what information about the nature of nonlinearity of a system
can be derived from measured higher-order frequency response functions?” First, the
existence of second-order frequency response functions indicates the existence of
nonsymmetric nonlinearity of a system a task that, for some systems such as 
and bilinear systems as mentioned before, cannot be achieved based on the analysis of
classical first-order frequency response functions. Secondly, as is discussed in some
detail next, parameters of a nonlinear system can also be identified based on the analysis
of higher-order frequency response functions together with the first-order ones 
In the following discussion, only the analysis of second-order frequency response
functions is presented. Depending on whether the physical parameters or the modal
parameters of the system are of interest, a ‘state-space analysis’ method 
or a 
space analysis’ method 
can be developed.

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3 Identification of Nonlinearity Using Higher-order 
102
as 
(where 
is the DC component which is supposed to be removed
and 
is the linear contribution), then, by replacing 
with 
equation (3-71) can be rewritten as