The influence of material parameters and geometry on an active junction

Paper in proceeding, 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.