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Long span bridges, with main spans beyond 2.000 m become highly
sensitive to wind action, particularly to flutter. An active aerodynamic control
method of suppressing flutter of very long span bridges is studied in this thesis.
Analytical design techniques for active control of the aeroelastic system
consisting of the bridge deck and two control surfaces are presented. These
techniques are based on a rational approximation of the unsteady aerodynamic
loads in the entire Laplace domain, which yieds matrix equations of motion with
constant coefficientes. The first part of this thesis is dedicated to the matrix
formulation of the rational functions known as Minimum State and to
applications to aerodynamic data obtained experimentally for various types of
bridge profiles. The precision of the approximations iscalculated, and plots of
the approximation functions compared to the available tabular data are drawn.
Next, the state-space equations of motion describing the aeroelastic behaviour
of a section of a bridge deck is presented. Given the dynamic data of a bridge
structure (mass, rotational mass moment of inertia, natural frequencies,
stiffness and damping ratios), and assuming that a geometric similitude exists
between the profiles of the full-scale bridge deck and the sectional model from
which the frequency dependent aerodynamic data was extracted, it is possible
to calculate the critical velocity of that particular bridge. This part of the thesis
shows that it is possible to build up a catalog of several profiles, characterized
by frequency dependent aerodynamic data and the corresponding rational
functions. The second part is dedicated to the formulation of the state-space
equations of motion describing the aeroelastic behaviour of the entire system
consisting of the bridge deck and control surfaces. The resulting equation
includes new aerodynamic states which model the air flow influence on the
moving deck. The equation of motion is a function of the mean velocity of the
incoming wind. The dependence of the equation of motion on the wind velocity
motivated the application of a constant and a variable-gain feedback concept to
the problem of flutter suppressing, which are presented separatelly. The output
variable-gain approach is formulated in terms of minimizing a performance
index dimensionally proportional to the sum of the work done by the rotating
control surfaces and the kinetic energy of the heaving velocity. A sistematic
method to determine the matrix of variable control gains is shown in detail, as
applied to the hypothethical case of Gibraltar bridge. Application of the variablegain
feedback concept was found to be very effective in suppressing flutter of
the bridge deck. Different geometric and dynamic characteristics can be
introduced in the MATLAB programs included in this work, in order to obtain the
critical velocities of a bridge deck alone, a bridge deck with stationary wings
and a bridge with moving wings activelly controled.