Longitudinal wave propagation in piezoelectric coupled rods

Abstract

This paper presents the results of longitudinal wave propagation in piezoelectric coupled rod structures. The deduction of non-dispersive or dispersive characteristics of the structures is based on a classical rod model and the Mindlin–Herrmann rod model. In the classical model, correction factors for piezoelectric effects are introduced to provide remedy for the discontinuity of the normal stress at the interface of the host rod and the piezoelectric layer. The non-dispersive characteristics of the structures, in which the piezoelectric effects are modelled are thus obtained by this classical model. The two-mode characteristics for the piezoelectric coupled rod structures are obtained by the Mindlin–Herrman model in which the lateral inertia is considered. This model is more accurate in predicting the dispersive characteristics of the structures. The results of the long- and short-wavelength limits are obtained as by-products. The results of phase velocity by the two models are agreeable at low wavenumber by adjusting the correction factor defined in the classical model. The results of this paper can serve as a reference for future study on wave propagation in coupled structures as well as in the design of smart structures incorporating piezoelectric materials.