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

In this paper, Bishop's 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 Bishop's 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.The advantages 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.

► A correction to Bishop's theory for longitudinal wave motion in bars is proposed.
► The correction provides a good estimate of the first-mode dispersion curve of the bar.
► The correction is also capable to predict adequately the transient response of the bar.
► The proposed method is versatile and simple to use.