Dispersion phenomena in coupled waveguides: veering, locking and strong coupling effects

The dispersion curves describe wave propagation in a structure. There might be a number of branches at a given frequency, each representing a wave mode. In complicated structures it is often tempting to interpret the dispersion curves in terms of waves in simpler structures. For example, waves in a fluid-filled cylinder might be interpreted as axial, bending or torsion waves in the in vacuo cylinder, or fluid waves in a rigid walled cylinder. The simpler wave modes are coupled in the real structure leading to complicated dispersion phenomena. This paper characterises these phenomena in general terms and discusses the circumstances under which they occur. Some are well known: propagating, evanescent and oscillatory attenuating waves, for which the wavenumber is real, imaginary or complex respectively, and cut-off of waves at some frequency. In more complicated structures weak coupling phenomena arise when branches of the dispersion curves interact. These occur in the vicinity of the frequency at which the dispersion curves in the uncoupled waveguides would cross: if two dispersion curves (representing either propagating or evanescent waves) come close together as frequency increases then the curves either veer apart or lock together, forming a pair of attenuating oscillatory waves, which may later unlock into a pair of either propagating or evanescent waves. Which phenomenon occurs depends on the product of the gradients of the dispersion curves. The wave mode shapes which describe the deformation of the structure under the passage of a wave change rapidly around this critical frequency. Other phenomena can be attributed to strong coupling effects, where arbitrarily light coupling changes the qualitative nature of the dispersion curves, and in particular the change from a pair of propagating or evanescent waves to evanescent or oscillatory attenuating waves. These effects are analysed, quantified, discussed and illustrated with examples. Copyright © (2011) by the International Institute of Acoustics & Vibration.