Antisymmetric Higher Order Edge Waves in Plates

This paper is concerned with the propagation of surface waves localized near the edge of plate (edge waves). Antisymmetric waves in a plate subject to traction free boundary conditions are considered. To study higher order edge waves three-dimensional equations of theory of elasticity are used. Asymptotic analysis is performed, which shows that there are an infinite spectrum of higher order edge waves. For the large values of wave number asymptotics of phase velocities are obtained. It is demonstrated that in the short-wave limit the phase velocities of all higher order edge waves tend to the velocities of Rayleigh wave, while the damping ratios tend to zero. Numerical results for first four higher order edge waves are presented in a wide frequency range.