Asymptotic Analytical Solution of Circumferential SH Wave in Functionally Graded Cylindrical Shell and Cylinder

Based on the basic equations of elasticity, the wave equations of functionally graded materials (FGM) cylindrical shell and cylinder are established in cylindrical coordinate system. Through different coordinate transformation of cylinder and cylindrical shell, the power series solution is obtained for the wave equation with variable coefficients, and the dispersion equation of circumferential SH wave propagation is obtained. We compare the power series solution and the accurate analytical solution of waves dispersion curves in the structures made of homogeneous material. It is shown that the power series solution and the accurate analytical solution have good agreement. The displacement amplitudes of SH waves in cylindrical shells with different thicknesses are calculated. The results show that the displacement amplitudes of cylinder and cylindrical shell is concentrated on the outer surface or sub-outer surface.