Active scattering control of flexural waves at beam junctions: The influence of beam properties on power flow and control effort

Journal article, 2008

As a wave, propagating in a beam, enters 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 the discontinuity. This phenomenon has been studied in the past, usually with the objective of changing the scattering properties of a free end. The purpose of this study is to investigate the effect of material parameters and cross-sectional dimensions on the control effort and power flow through a beam discontinuity, given a certain control objective. Active scattering factors, based on Euler–Bernoulli theory, are derived for the junction of two beams, with rectangular cross-sections. Desired constraints are put on one or several of these scattering factors and the equivalent required force is calculated. The control objectives studied are: a non-reflective junction, a non-transmissive junction and the minimisation of power flowing from the junction back into the beams. Derived expressions show that the control forces can, after normalisation, be expressed in a two-dimensional space (plane) for all possible material parameter and cross-sectional dimension combinations. In their limits these planes also contain the ideal termination cases. Thus, e.g. the required control forces in order to achieve a non-reflective junction for a clamped or free beam end are covered by these results. The transmission and reflection efficiencies for the different control objectives can also be depicted in the same plane. Results indicate the possibility of choosing a right-side beam and active force combination in such a way that the junction is anechoic and absorptive.