This article presents the analytical linearization of aerodynamic loads (computed with the
unsteady vortex-lattice method), which is formulated as tangent matrices with respect to the
kinematic states of the aerodynamic grid. The loads and their linearization are then mapped
to a nonlinear structural model by means of radial-basis functions allowing for a two-way
strong interaction scheme. The structural model comprises geometrically exact beams formulated
in a director-based total Lagrangian description, circumventing the need for rotational
degrees of freedom. The structural model is spatially discretized into finite elements and
temporally discretized with the help of an implicit scheme that identically preserves momenta
and energy. The resulting nonlinear discrete equations are solved by applying Newton’s
method, requiring calculating the Jacobians of the whole aeroelastic system. The correctness
of the linearized loads is then shown by direct comparison with their numerical counterparts.
In addition, we employ our strongly-coupled aeroelastic model to investigate the nonlinear
static and dynamic behavior of a suspension bridge. With this approach, we successfully investigate
the numerical features of the aeroelastic system under divergence and flutter conditions.
|