Identification of the dynamic characteristics of nonlinear structures

3
Identifkation of Nonlinearity Using Higher-order 
98
Time History
Power Spectrum
Fig.3.15 Time History and Power Spectrum of a Band-limited Input Signal
Again, as in the case of second-order Volterra kernel transform measurement, the 
order Wiener kernel transforms of the square-law system, the SDOF nonlinear system,
the 3DOF nonlinear system and a bilinear system are calculated and are shown in
Also, as a typical example, the second Wiener kernel (time domain) of
the SDOF system is illustrated in Fig.3.20. When comparing the measured frequency
response functions (Wiener kernel transforms) with their corresponding analytical
Volterra kernel transforms (figs.35 3.9 3.1 it can be seen that the results are quite
good. For the bilinear system, the measured second-order frequency response function
looks very much like the second-order frequency response functions of the square-law
system. Therefore, for a bilinear system, the quadratic component is quite substantial in
the response x(t). However, it should be pointed out that although the linear contribution
can theoretically be averaged out by including sufficient data points (increasing the
averaging time), this is often difficult to do in practice since the computation resources
required are considerable. During calculation of the second-order Wiener kernels of the
SDOF and the 3DOF nonlinear systems, the linear contributions (the response component
due to the linear part of the nonlinear network) are removed first before the correlation
process takes place because the convergence seems to be very slow in these cases. In
order to calculate second-order Wiener kernels of a nonlinear system efficiently, removal
of the linear contribution becomes necessary. A possible way of removing linear
contribution and therefore increasing the computational efficiency is proposed and
discussed next.

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3 Identification of Nonlinearity Using Higher-order 
99
Measured Second Order FRF of the Square-law System Using Correlation
(Modulus Linear Scale, x-axis 
-275 
275, y-axis 
-275 
275 
Eg.3.17 
Measured Second Order FRF of the 
SDOF Nonlinear System Using Correlation
Analysis (Modulus Linear Scale, x-axis 
-275 
275, y-axis 
-275 
275 

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3
of Nonlinearity Using Higher-order 
100
Measured Second Order FRF of the 3DOF Nonlinear System Using Correlation
Analysis (Modulus Linear Scale, x-axis 
-275 275, y-axis 
-275 275 
Measured Second Order FRF of a Bilinear System Using Correlation
Analysis (Modulus Linear Scale, x-axis 
-275 275, y-axis 
-275 275 

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