Affiliations: Dipartimento di Meccanica, Politecnico di Torino,
Torino, Itlay
Note: [] Corresponding author: L. Garibaldi, Dipartimento di Meccanica,
Politecnico di Torino, Corso Duca degli Abruzzi, 24, Torino, Italy. E-mail:
[email protected]
Abstract: It is well known that nonlinear systems, as well as linear
time-varying systems, are characterized by non-stationary response signals. In
this sense, they both show natural frequencies that are not constant over time;
this variation has however different origins: for a time-varying system the
mass, and possibly the stiffness distributions, are changing over time, while
for a nonlinear system the natural frequencies are amplitude-dependent. An
interesting case of time-varying system occurs when analyzing the transit of a
train over a railway bridge, easily simulated by the crossing of a moving load
over a beam. In this case, the presence of a nonlinearity in the beam behaviour
can cause a significant alteration of the modal parameters extracted from the
linearized model, such that the contributions of the two effects are no more
distinguishable. For this study, some reinforced concrete beams have been
tested in the framework of a vast project: these beams show a clear softening
nonlinear behaviour, well detectable when the excitation is produced by a
hammer (free response). If the passage of a carriage is considered, moreover,
the variation of natural frequencies is always larger than expected because of
this softening nonlinearity. The article first analyzes theoretically the two effects on the
natural frequencies of a simply supported beam, then a numerical and an
experimental tests are presented. The identification procedure is conducted
with a linear algorithm called ST-SSI, which has been demonstrated to be
appropriate for the analysis of non-stationary signals, in particular in
presence of moving masses. The article shows that the nonlinear contribution
can be well estimated by using this linear tool but, on the contrary, when also
moving masses are present, it is difficult to separate the nonlinear effects
from the time varying ones.
Keywords: Moving load, nonlinear behaviour, Short Time Stochastic Subspace Identification, concrete reinforced beams
