Revisiting the Love hypothesis for introducing dispersion of longitudinal waves in elastic rods (Q6540439)

The paper deals with the problem of dispersion of longitudinal waves in cylindrical elastic rods. The so-called Love equation and its different variants are investigated based upon the linear elasticity theory. An alternative is suggested using multi-scale approximation by introducing slow time scale. This leads to the refined Love equation. The result coincides with earlier models in the leading order. The governing equation of disturbance becomes the linear KdV equation. The graphical representations show that the frequency spectrum is very similar to that of the linear KdV equation.