Identification of the dynamic characteristics of nonlinear structures

2 Identification of Nonlinearity Using First-order 
23
2.3.1 DETECTION OF NONLINEARITY BY DIRECTLY
USING FRF DATA
As far as nonlinearity detection is concerned, many techniques are available. The simplest
methods are those which are based on the use of raw measured frequency response data
without any post-measurement data processing. Detection techniques of this type are the
Bode plot and the reciprocal receptance plot methods.
The basis of using Bode and or reciprocal receptance plot methods to detect nonlinearity
is that, due to the existence of nonlinearity, the measured first-order 
will be
distorted systematically from the corresponding linear frequency response functions.
Since linear 
are very well 
the existence of nonlinearity can be revealed
by examining the abnormal behaviour of the measured first-order 
To illustrate use of the Bode plot to detect nonlinearity, frequency response functions
measured from a practical Beam/Absorber nonlinear structure are used. As shown in
Fig.2.1, when the excitation force level increases, the distortion in the measured FRF
data also increases and the apparent resonance frequency (the frequency of maximum
FRF value) drops. The existence of softening stiffness nonlinearity of the structure is
clearly demonstrated.
1 8 5 . 0 0
Frequency 
H z .
Fig. 2.1 FRF Data Measured from Practical Beam-absorber Structure
As an alternative but more versatile technique, FRF data can be displayed in their
reciprocal form to detect the existence of nonlinearity. The advantage of displaying data in

---

2
Identification of Nonlinearity Using First-order 
2 4
this format is that, in the case when the modal constant of the mode be analysed is
effectively real, this technique can not only detect the existence of nonlinearity, but can
also give an indication as to whether the nonlinearity exists in the stiffness or damping.
Suppose the residual contribution of other modes has been subtracted or can be neglected,
the receptance data around 
mode of the structure can be expressed as