A study of the secular equation for rayleigh waves using the root locus method

In a recent note Rahman and Barber Trans. ASME 62 (1995) 250] proposed an exact expression for the roots of the secular equation for the Rayleigh waves in an isotropic half-space. Using the root locus method, we describe in a very simpler manner the evolution of the roots versus the Poisson's ratio and we derive easily the critical value for which the nature of the roots changes.