PhDThe identification of the dynamic characteristics of nonlinear
systems is of increasing interest in the field of modal testing.
In this work an investigation has been carried out into the
force-state mapping approach to identification of nonlinear
systems proposed by Masri and Caughey. They originally suggested a
nonparametric identification technique based on curve fitting the
restoring force in terms of the velocity and displacement using
two dimensional Chebyshev polynomials. It has been shown that the
use of Chebyshev polynomials is unnecessarily restrictive and that
a simpler approach based on ordinary polynomials and special
functions provides a simpler, faster and more accurate
identification for polynomial and nonpolynomial types of
nonlinearity. This simpler approach has allowed the iterative
identification technique for multi-degree of freedom systems to be
simplified and a direct identification approach, which is not
subject to bias errors, has been suggested.
A new procedure for identifying both the type and location of
nonlinear elements in lumped parameter systems has been developed
and has yielded encouraging results.
The practical implementation of the force-state mapping technique
required the force, acceleration, velocity and displacement
signals to be available at the same instants of time for each
measurement station. In order to minimise the instrumentation
required, only the force and acceleration are measured and the
remaining signals are estimated by integrating the acceleration.
The integration problem has been investigated using several
approaches both in the frequency and time domains.
An analysis of the sensitivity of the estimated parameters with
respect to any amplitude and phase measurement errors has been
carried out for single-d.o.f. linear systems. Estimates are shown
to be extremely sensitive to phase errors for lightly damped
structures.
The estimation of the mass or generalised mass and modal matrices
required for the identification of single or multi-d.o.f.
nonlinear systems respectively, has also been investigated.
Initial estimates were obtained using a linear multi-point force
appropriation method, normally used for the excitation of normal
modes. These estimates were then refined using a new technique
based on studying the sensitivity of the mass with respect to the
estimated system parameters obtained using a nonlinear model. This
sensitivity approach seemed promising since accurate results were
obtained. It was also shown that accurate estimates for the modal
matrix were not essential for carrying out a force-state mapping
identification.
Finally, the technique has been applied experimentally to the
identification of a cantilevered T-beam structure with stiffness
and damping nonlinearity. The cases of two well separated and then
two fairly close modes were considered. Reasonable agreement
between the behaviour of the nonlinear mathematical model and the
structure was achieved considering inaccuracies in the measurement
set-up.
Conclusions have been drawn and some ideas for future work
presented.Scientific Studies and Research Centre of Syri
