The influence of material parameters and geometry on an active junction
Paper in proceedings, 2007
As a wave propagating in a beam enters upon a discontinuity it will be partly reflected and partly
transmitted. The introduction of an external force can be used to impose restrictions on the scattering
properties of this discontinuity. This phenomenon has been studied in the past, usually in
the form of a free beam end. Thus the objective has been to change the reflection properties at
the boundary. The purpose of this study is to investigate the control effort and power flow trough
a beam discontinuity, for arbitrary material parameters and geometry. Active scattering factors,
based on Euler-Bernoulli theory, are derived for the junction of two beams. Desired constraints are
put on one or several of these scattering factors and the equivalent required force is calculated.
The derived force is purely analytical function of the material parameters and geometry of the
beams. The control objectives studied are, no reflection or, no transmission at the discontinuity
and the minimisation of power flowing away from the discontinuity. Results show that every possible
material parameter and geometry combination can be covered in a two-dimensional space,
enabling easy depiction of control effort for the derived control forces.