An explicit secular equation of Rayleigh waves propagating along an obliquely cut surface in a directional fiber-reinforced composite

The propagation of Rayleigh waves along an obliquely cut surface in a directional fiber-reinforced composite was studied recently by Ohyoshi [Ohyoshi T. Compos Sci Technol 2000; 60; 2191-6]. The author derived the secular equation of the wave, however, it is still implicit. In this paper, a fully explicit secular equation of the wave is obtained by using the method of first integrals. From it we immediately arrive at the secular equation of the wave for the case when the cut surface is parallel to the fiber direction. This secular equation is much more simple than the ones obtained recently by Cerv [Cerv J. Int Rev Mech Eng (IREME) 2008; 2; 762-72] and Cerv et al. [Cerv J et al. Composite Structures 2010; 92; 568-77]. Based on the obtained secular equations some approximate formulas for the velocity of Rayleigh waves are established and it is shown that they are good approximations. The explicit secular equations and the approximate formulas for the velocity derived in this paper are useful for analyzing the effect of the material properties and the orientation of the fiber direction on the Rayleigh wave velocity, especially they are powerful tools for solving the inverse problem: determining the material parameters from the measured values of the velocity