Identification of the dynamic characteristics of nonlinear structures

2 Identification of Nonlinearity Using First-order 
50
Damping 
N a t u r a l
.
 1. 
itudc
of Modal Const
Phase Angle of Modal Const
.
.
I
J
.
.
1 
1. SSE-04
Rcrp. Amplitude
Modal Parameters versus Vibration Amplitude
When the method is applied to the study of damping nonlinearity, the results are as
encouraging as those for stiffness nonlinearity. As shown in Fig.2.19, the existence of
dry friction damping can be suspected from the characteristic oval-shaped Nyquist plot
and the distorted damping plot. As in the stiffness nonlinearity case, frequency response
data measured from an analogue computer circuit with simulated frictional damping are
analysed using this new method and the results shown in Fig.2.20. The damping
coefficient decreases as response amplitude increases, which indicates damping of dry
friction nature.

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 of Nonlinearity Using First-order 
51
X
X
X
X
X
Nyquist and Damping Plot of FRF Data with Frictional Damping
N a t u r a l
g 
itude
Modulus of Modal Conrt
itudc
 
Phase 
of Modal Const
Rasp. Amplitude
Fig.20 Modal Parameters 
Vibration Amplitude (Simulated Friction Damping)
The 
box contains three circuits of unknown nonlinear SDOF systems and its
purpose is to see whether these unknown nonlinear systems can be identified. The 
data measured from one of the systems and the calculated damping plot are shown in

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2
Identification of Nonlinearity Using First-order 
52
Fig.2.21. From these results, the existence of a stiffness nonlinearity is 
By
analysing the FRF data using the new method, the curves of natural frequency and
damping coefficient response amplitude can be established as shown in Fig.2.22. As
compared with the numerical calculation results of figure 2.15, it can be concluded that
the system possesses backlash stiffness nonlinearity.
Fig.2.2 1 FRF and Damping Plot of 
Box Data