Correction to Bishopʹs approximate method for the propagation of longitudinal waves in bars of generic cross-section

In this paper, Bishopʹs procedure for the assessment of longitudinal wave motion in elastic bars is enhanced by rectifying some discrepancies that appear in the assumptions and results of Bishopʹs theory. The proposed correction leads to a significant improvement in predicting the first-mode dispersion curve of a bar, as shown by comparison with experimental data. Furthermore, the simple differential equation of motion derived from this correction is proven to give an adequate estimate of the transient response of a bar under dynamic excitation. vantages of the present formulation over other existing theories are twofold. Firstly, it can be applied to bars of any cross-section. Secondly, and more importantly, its treatment is straightforward and its results – like the dispersion relation and the differential equation of motion it provides – are easy to use in practical applications.