IMPERIAL
COLLEGE OF SCIENCE, TECHNOLOGY
AND MEDICINE
University of London
IDENTIFICATION OF THE
DYNAMIC CHARACTERISTICS OF
NONLINEAR STRUCTURES
Rongming Lin
A thesis submitted to
the University of London for
the degree of Doctor of Philosophy and for
the Diploma of Imperial College.
Dynamics Section
Department of Mechanical Engineering
Imperial College of Science, Technology and Medicine
London SW7
December 1990
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ABSTRACT
Modal analysis has been extensively developed during
the last two decades and has
become one of the most effective means of identifying the dynamic characteristics of
engineering structures. However, most of the techniques developed so far are based on
the assumption that the structures to be identified are linear while, in practice, most
engineering structures are
nonlinear.
It is therefore necessary
to extend existing linear
modal analysis techniques or develop new techniques so that structural nonlinearity can
be
detected, quantified
and
mathematically
based on the measured input-output
dynamic characteristics. This thesis seeks to present complete yet new developments on
the identification of dynamic characteristics of nonlinear structures.
For nonlinear structures whose modal parameters for certain modes are displacement
dependent (the nonlinearity is of symmetrical type), a
new nonlinear modal analysis
method based on the measured first-order frequency response functions is developed.
The method has been effectively applied to the data measured from practical nonlinear
structures even when the modes become considerably complex. On the other hand, for
structures whose nonlinearities are such that the measured first-order frequency response
functions are effectively linear (nonlinearity of nonsymmetrical type), a higher-order
frequency response function analysis is presented which provides opportunities for the
identification of such nonlinear structures. Both the first-
and higher-order frequency
response function analyses are based on the classical assumption that the output of a
nonlinear structure is periodic if the input is periodic. However, for some nonlinear
systems (chaotic systems), this assumption is no longer valid and special techniques need
to be developed in order to identify them. In this thesis, 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 systems are presented. Both numerical studies and experimental
investigations are carried out and possible engineering applications are discussed.
It is believed that nonlinearities of most engineering
structures are usually
in just
a few spatial coordinates and the ability to locate these has some important engineering
applications. In this thesis, location techniques based on the correlation between analytical
model and measured modal parameters as well as frequency response data are developed.
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Numerical study and
investigation demonstrate the practical applicability of
these techniques. Because of the limitation
of measured data available, it is essential to
pinpoint where the structural nonlinearity is located before a nonlinear mathematical
model can be established.
The ultimate target of the analysis of a nonlinear structure is to establish a nonlinear
mathematical model (spatial model) which is a function of response amplitude. It is
believed that such a target can only be achieved by combining analytical modelling (FE
modelling) and modal testing techniques. In this thesis, new model updating methods are
developed and extended to the mathematical modelling of nonlinear
structures based on
the correlation between analytical and measured modal parameters as well as frequency
response data. The practical applicability of these methods is assessed based on a specific
case study. 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 sufficient to solve the model updating problem uniquely.
