Identification of the dynamic characteristics of nonlinear structures

158
Current
Current I
Force F 
Amplifier
I
I
I
I
Fig.5 16 Amplifier Shaker Unit
Fig.517 Characteristics of Amplifier-shaker Unit around Structural Resonance
ANALOGUE CIRCUIT
The simulated stiffness nonlinearity is required to be a cubic stiffness described by
and the acceleration signal is proportional to the displacement signal when
sinusoidal input is considered. Therefore, the analogue circuit is required simply to
multiply the input signal twice to obtain a 
output as shown in Fig.5.18.
Analogue Computer Circuit

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5
Location of Structural Nonlinearity
159
MEASUREMENT SETUP
The measurement setup is illustrated in 
19. A Solartron 1254 Frequency Analyser
was used to obtain the frequency response functions of the structure and an HP 9816
computer was used to store and analyse the measured data.
current power 
low-pass filter
charge amplifier
test 
structure
charge amplifier
fier
low-pass filter
analogue circuit
Fig.5.18 Measurement Setup

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5
 of Structural Nonlinearity
160
5.4.2 MEASUREMENT RESULTS
As a preliminary measurement, the frame was tested without the nonlinear SDOF system
(shaker) attached. All 20 translational coordinates around the frame were measured using
sinusoidal excitation in the frequency range of 
with excitation at coordinate 
(figure 5.14). The calibration results of the measurement system and typical frequency
response functions measured are shown in 
In the measurement
frequency range of 
6 modes were clearly identified (the first resonance is in
fact two close modes as shown in Fig.5.21). All these modes were analysed and the
modal parameters are tabulated in Table 5.1 (in modal analysis, the first two close modes
were treated as single mode because the frequency resolution of the measured FRF data is
not enough for them to be accurately identified and it is not our purpose to do so).