Results On Transversal And Axial Motions Of A System Of Two Beams Coupled To A Joint Through Two Legs

Abstract

In recent years there has been renewed interest in inflatable-rigidizable space structures
because of the efficiency they offer in packaging during boost-to-orbit.1 However, much
research is still needed to better understand dynamic response characteristics, including inherent
damping, of truss structures fabricated with these advanced material systems. We present
results of an ongoing research related to a model consisting of an assembly of two beams with
Kelvin-Voight damping, coupled to a simple joint through two legs. The beams are clamped
at one end but at the other end they satisfy a boundary condition given in terms of an ODE
coupling boundary terms of both beams, which reflects geometric compatibility conditions. The
system is then written as a second order differential equation in an appropriate Hilbert space
in which well-posedness, exponential stability as well as other regularity properties of the solutions
can be obtained. Two different finite dimensional approximation schemes for the solutions
of the system are presented. Numerical results are presented and comparisons are made.