Time-Harmonic Dynamics of Curved Beams

Wave propagation along a curved Euler-Bernoulli beam is considered. The dispersion relation is derived and its roots are given in analytical form and described in the complex plane. In contrast to straight beams, in the low-frequency regime three propagating modes coexist and a special zero-frequency bifurcated configuration is present, when the wavenumber magnitude is equal to the curvature of the centroid axis of the structure. The first frequency regime is followed by a second regime where a single propagating mode is present, in which longitudinal and transverse waves are strongly coupled. The broadband coupling between longitudinal and transverse waves is also quantified. Finally the transmission properties of the structure are characterized evidencing a transition between a low and high frequency regime. In the low frequency/high curvature regimes strong coupling between longitudinal and transverse mode is present, while in the high frequency/low curvature regime such coupling is absent.