Identification of the dynamic characteristics of nonlinear structures

 =
A, + 
 + 
 =
A, + 
 + 
(2-48)
Because equations (2-48) and (2-49) are complex algebraic equations, the four modal
parameters 
A, and 
can be determined. These parameters represent the linear
model which corresponds to the chosen response amplitude. By examining different point
pairs similar to 
and 
the characteristics 
and 
of the
original nonlinear structure against vibration amplitude can be revealed.
2 . 5 . 3 APPLICATION OF THE NEW METHOD TO THE ANALYSIS OF
NONLINEAR SYSTEMS SIMULATED
USING ANALOGUE CIRCUITS
The above method has been applied to several systems with various types of nonlinear
stiffness or damping in order to assess fully the feasibility of the method. As an
alternative means of solving nonlinear differential equations numerically, analogue
circuits have been constructed to simulate nonlinear SDOF systems. Analogue computer
data with cubic stiffness and frictional damping as well as FRF data measured from
the 
box (an electrical analogue computer device built to simulate nonlinearity)
are employed and analysed.
For the case of a cubic stiffness nonlinearity, receptance 
data with constant force
input together with the calculated isometric damping plot are shown in Fig.2.17. From
figure 2.17, the jump phenomenon which is typical of stiffness nonlinearity is clearly
demonstrated and the isometric damping plot shows a well-defined surface distortion
pattern. It can be seen that the nonlinearity is clearly indicated both from the receptance
data plot and the damping plot. practice, however, what is required is the quantification
of the nonlinearity and not just its detection. By using this new method, the system’s
properties in terms of modal parameters versus response amplitude have been obtained as
shown in Fig.2.18, from which it can be concluded that the damping is linear since the

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2 Identification of Nonlinearity Using First-order 
49
damping coefficient does not change with response amplitude, while the stiffness is
nonlinear 
the 
of nonlinearity is quantified in the natural frequency versus
response amplitude plot.
from CUBE25875
Hz.
Fig.2.17 FRF and Damping Plot of Analogue Computer Data

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