Approaches to estimating the reflection and transmission coefficients of discontinuities in waveguides from measured data

The vibration modelling of waveguides is relevant to many engineering applications. Although there are many prediction techniques available, at present a fundamental weakness can undermine all of them; this weakness arises from inadequate modelling of joints and discontinuities due to uncertainty in joint properties and behaviour. An approach to joint parameter estimation from vibration measurements, which makes use of wave models of waveguide systems, has been proposed previously. In this paper, a number of approaches to estimating the reflection and transmission coefficients of a joint from measured data are developed. Of particular interest is the case where only a limited set of measured data is available. Initially a generalized joint in a waveguide system, which may support many wavetypes, is considered. Further insights into the behaviour of such a system are then gained by examining a much simpler system in which only one wavetype can exist. Finally, measurements are made on a beam with a mass/moment of inertia discontinuity and on a pipe with a right-angled bend, both with flexural excitation, in order to demonstrate the procedures and to highlight some of the inherent difficulties.