Locking and veering in periodically coupled, homogeneous waveguides and application to two coupled beams

Wave propagation in periodic waveguides exhibits well-known pass and stop band behaviour, frequency bands where waves propagate freely or attenuate. This paper concerns two further phenomena - veering and locking - which occur in more complex waveguides where two or more wave modes exist. The analysis specifically concerns two, periodically point-coupled waveguides, which themselves may have periodic construction. The particular case of two point-coupled beams is considered as an example and numerical results presented. The veering and locking phenomena occur around critical points where the dispersion curves of the uncoupled-blocked systems intersect. Veering occurs if these uncoupled dispersion curves have the same slope at the critical point: two propagating wave modes remain propagating in the coupled system. Locking occurs if they have opposite slopes: two propagating wave modes lock together, becoming a pair of attenuating wave modes and an additional stop band is produced. These effects are common in periodic structures in which two or more wave modes exist because free waves involve an infinite sum of space-harmonic components, propagating in both positive and negative directions, and the dispersion curves frequently intersect. Experimental results taken from two, spring-coupled beams are presented to illustrate the behaviour. Frequency response measurements were taken at the same point in a number of adjacent periodic cells. Under the assumption of a known number of Bloch waves propagating in both directions in the structure, the measurements from this array of points on the beam are post-processed using a least-squares procedure to provide estimates of the propagation constants in the coupled system, these estimates agreeing well with predictions especially for propagating and slowly-attenuating Bloch waves.