Identification of the dynamic characteristics of nonlinear structures

2 Identification of Nonlinearity Using First-order 
58
where 
is the modal constant of
the mode to be analysed) were analysed using this proposed nonlinear modal analysis
method and the results are shown in Fig.2.28. As compared with figure 2.20, the
analysis results obtained are very similar indeed.
Damping Coeff 
N a t u r a l
,
to
 
 
 
R e s p . A m p l i t u d e
M o d u l u s o f M o d a l C o n s t
P h a s e A n g l e o f M o d a l C o n s t
 _
.
R e s p .
R e s p .
i t u d e
Fig.2.28 Analysis Results of Frictional Damping with 1% Residual
2.5.5 APPLICATION OF THE METHOD TO PRACTICAL
NONLINEAR STRUCTURES
The proposed new method has so far been successfully applied to the analysis of FRF
data measured from nonlinear analogue circuits and analytically-generated FRF data for
nonlinear MDOF systems. The assessment of residual effects on analysis accuracy has
also been carried out. The method is now applied to the analysis of practical nonlinear

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2 Identifkation of Nonlinearity Using First-order 
59
structures. First-order FRF data measured from three different practical structures
(Beam/Absorber, Frame and NASTRAN Tower structures) are to be analysed.
The Beam/Absorber structure as shown in Fig.2.12 was designed for the experimental
investigation of dynamic absorber systems. Some typical measured FRF data with
constant force input are illustrated in Fig.2.29. In addition to the shift of resonance
frequency which indicates the existence of a stiffness nonlinearity, the mode to be
analysed is markedly complex (about 
phase rotation of the Nyquist circle). One of the
FRF curves shown in figure 2.29 was analysed using the proposed method and the
results are shown in Fig.2.30. From the natural frequency response amplitude curve,
it can be deduced that the structure probably possesses softening backlash stiffness
nonlinearity which is physically due to the fact that, when the response amplitude
increases, the supports at both ends of the beam (see 
go from micro-slip
(stiffness 
to slip (stiffness 
which reduces the system’s stiffness and so
the natural frequencies.
Fig.2.29
of Beam/Absorber Structure

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2
Identification of Nonlinearity Using First-order