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1.5 PREVIEW OF THE THESIS
Despite rapid developments in the identification of dynamic characteristics of linear
structures in recent decades, structural nonlinearity presents a major difficulty to the
majority of applications to practical cases. The research presented in this thesis is intended
to seek new developments on the identification, location and modelling of structural
nonlinearities in the pursuit of better understanding of the dynamic characteristics of
practical nonlinear structures.
Based on the analysis of measured first-order
some of the recently-developed
techniques for the identification of nonlinearity are reviewed in Chapter 2 and their
advantages and disadvantages when applied to practical problems are discussed. Then, a
new improved method for the nonlinear modal analysis of complex modes is developed to
cope with the practical situations in which measured modes become complex. The method
has been successfully applied to the data measured from practical nonlinear structures
Introduction
10
even when the modes are considerably complex.
the other hand, for structures whose
nonlinearities are such that the measured first-order
are effectively linear (the
nonlinearity being of nonsymmetrical type), a higher-order frequency response function
analysis becomes necessary for the identification of such nonlinear structures. The
theoretical basis of higher-order FRF analysis is presented in Chapter 3 with special
attention given to the numerical assessment of the practical applicability the technique.
Both
and higher-order FRF analysis techniques are largely based on the classical
assumption that the output of a nonlinear structure is periodic if the input is periodic. For
some nonlinear systems however, this assumption is no longer
(chaotic systems, in
which a periodic input will result in an output of “random” nature) and special techniques
need to be developed in order to identify them. In Chapter 4, for the first time, the hidden
chaotic behaviour of a mechanical backlash system with realistic system parameters has
been revealed and, based on this system, qualitative as well as quantitative ways of
identifying chaotic structures are presented. Both numerical studies and experimental
investigations are carried out and possible engineering applications are discussed.
It is believed that nonlinearity in most engineering structures is usually
in certain
spatial coordinates and the ability to locate these has some important engineering
applications. In Chapter 5, nonlinearity location techniques based on the correlation
between an analytical model and measured modal parameters and/or measured frequency
response function data are developed. Numerical studies and experimental investigation
demonstrate the practical applicability of these techniques.
The ultimate target of the analysis of a nonlinear structure is to establish a nonlinear
mathematical model which is a function of response amplitude. It is believed that such a
goal can only be achieved by combining analytical modelling (FE modelling) and
experimental modal testing techniques. In Chapter 6, a new model updating method is
developed and extended to the mathematical modelling of nonlinear structures based on
the correlation between an analytical model (of a linear system) and measured frequency
response data. As compared with existing methods, the new method shows marked
advantages. The practical applicability of the method is assessed based a special case
study. In Chapter 7, criteria on minimum data required in order to update an analytical
model are established and the possibilities and limitations of analytical model
improvement are discussed which make it possible for the analyst to judge whether a set
of measured data will be adequate to solve the model updating problem uniquely.
Finally, Chapter 8 reviews
the new developments presented in this thesis and indicates
the direction for possible further studies.
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