Identification of the dynamic characteristics of nonlinear structures

 
 
 
 
 

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2 Identification of Nonlinearity Using First-order 
2 2
then identified satisfactorily. For most nonlinear structures in practice, relatively high
excitation levels are recommended. For some others, such as structures with frictional
damping, the situation can be the other way round and in order to identify such
nonlinearities, the excitation levels should be set as low as possible. Lastly, for structures
whose nonlinearities have no effect on the measured first-order 
the measurement
of higher-order 
is recommended.
2.3
RECENT DEVELOPMENTS ON THE IDENTIFICATION OF
NONLINEARITY BASED ON THE FIRST-ORDER
FREQUENCY RESPONSE FUNCTIONS
Once a structure is suspected of being nonlinear and its first-order 
are measured as
discussed above, it becomes necessary to take nonlinearity into account in the subsequent
modal analysis of the data. In practical nonlinearity analysis, in order to understand the
nature and extent of nonlinearity, three requirements must be achieved by appropriate
application of modal analysis methods. First, the existence of nonlinearity needs to be
detected. Second, the extent of the nonlinearity needs to be quantified. Finally, physical
characteristics of nonlinearity need to be established.
It is believed that the first requirement (detection) is comparatively easy to achieve. In
fact, simply by comparing the difference between measured frequency response functions
at different excitation levels, the existence of nonlinearity can be discovered. The
quantification of nonlinearity, that is the establishment of the relationship between modal
parameters and response levels based on the measured first-order 
is the main topic
of this chapter and will be discussed in detail. The last objective and the most difficult
task in nonlinear modal analysis is the identification of physical characteristics of
nonlinearity the relationship between the structural spatial properties (such as stiffness)
and response amplitudes. As will be shown in chapter 6, the establishment of such a
nonlinear spatial model can only be achieved based on the correlation between the
analytical model and vibration test data.
In efforts to achieve these various objectives of nonlinearity analysis, a large number of
papers have been published in recent years. Methods which are commonly used in
practical nonlinear modal analysis are to be reviewed and their advantages and
disadvantages will be discussed.

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