Abstract：Wave propagations of the shear horizontal (SH) wave in a bi-directional functionally graded (BDFG) infinite plate are investigated. The frequency equation is obtained for a BDFG infinite plate with traction free plate faces and the dispersion curves are presented. Numerical results shows that the gradient index has significant effect on the dispersion curves for low branches, while has little effect on those for high branches. When the material is uniform in the x-direction (the in-plane wave propagation direction) but changes exponentially in the z-direction (thickness direction), the dispersion characteristics of SH waves in functionally graded plates are similar to those in uniform plates. As for the gradient index in the z-direction takes different values, there always exists a branch of the dispersion curve where both the phase velocity and group velocity are equal to the shear wave velocity. When the material changes exponentially in the x direction, there is no dispersion curve branch where the phase velocity and group velocity are equal to the shear wave velocity. For each given angular frequency, it always corresponds to a complex wave number, indicating that SH waves will exhibit certain attenuation characteristics when propagating in the x-direction. This investigation has positive significance for parameter inversion of functionally graded materials by using SH waves.
2026, Vol. 47 
