Identification of the dynamic characteristics of nonlinear structures

2 Identification of Nonlinearity Using First-order 
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Fig.2.7 Analysis of Stiffness Nonlinearity Using Inverse Receptance Method
1
However, an assumption that the modal constant of the mode to be analysed should be
real and 
was made during the development of the Inverse Receptance method.
The validity of this assumption when analysing FRF data measured from practical
nonlinear structures will be discussed later on but, the influence of mode complexity on
the estimation of 
and 
based on this method will be discussed here. Suppose
the modal constant is complex and can be expressed as 
then equations (2-
14) and (2-15) becomes:
= 
+ 
sine)
(2-16)
=
 
(2-17)
Comparing equations (2-16) and (2-17) with those of (2-14) and 
and bearing in
mind that modal parameter changes due to nonlinearity are usually of second order, a
small degree of complexity could seriously impair the results obtained based on the
Inverse Receptance method just outlined. To illustrate this point, the same FRF data as
those shown in Fig.2.7, but with 
modal constant complexity artificially added are
analysed using the method and the results are shown in Fig.2.8. In this case, not only is
damping value seriously in error (it should be constant for data points on either side of
the resonance since the damping is linear), the calculated natural frequencies are incorrect
as well (compare with figure 2.7). This demonstrates the limitation of the Inverse
Receptance method and recommends the necessity of further development so that
nonlinearity can be analysed accurately when measured modes become complex.

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