Dynamic response of a functionally graded cylindrical tube with power-law varying properties due to SH-waves

An analytical solution to the dynamic response of a functionally graded cylindrical tube embedded in a full homogeneous space subjected to elastic SH waves is presented using the wavefunction expansion method. The shear modulus of the functionally graded tube is assumed to have a power-law variation with radius. The wave fields in the tube and unbounded surrounding medium are derived in a form of wavefunction series with unknown coefficients. The wave field coefficients are obtained by satisfying the boundary conditions at the inner and outer tube surfaces. The influences of the inhomogeneity exponent, shear modulus and thickness of the functionally graded tube, and the frequency of the incident SH waves on the dynamic stress concentration factor (DSCF) of the tube are systematically discussed. It is concluded that the application of functionally graded materials (FGMs) with a positive inhomogeneity exponent tends to weaken the DSCF along the inner surface of the tube significantly but intensify that along the outer surface slightly, which is beneficial to the long-term use of the tube.