Elastic wave propagation analysis in a 2d functionally graded hollow cylinder using spectral finite element method

Functionally graded material (FGM) is a kind of special composite which components and material properties vary continuously along some directions. The material has been used in aerospace, nuclear, military and automotive industry fields because of its excellent designability and mechanical performance at the interface. In those applications, transient dynamic response analysis is an important problem, especially for structural health monitoring or impact load identification. A two-dimensional axisymmetric element is proposed to simulate the wave propagation in functionally graded cylinders, which is established by time-domain spectral finite method (SFEM). The interpolation nodes of the element are collocated at the Gauss-Lobatto-Legendre (GLL) points to avoid the Runge phenomenon and get high accuracy. Besides, the mass matrix is diagonal due to the orthogonality of the approximation functions. Hence, the time-domain SFEM is more effective compared to the conventional FEM for wave propagation problems. In addition, the high-order shape functions used in SFEM can give better approximation of varying material properties. Therefore, the time-domain SFEM is particularly suitable for wave propagation analyzes of complex FGM structures. Elastic wave propagation in a functionally graded cylinder subjected to an impulsive loading is studied detailed. The effect of material grading pattern is analyzed. The results demonstrate the effectiveness of the present method for the analysis of elastic wave propagation in functionally graded solids with axial symmetry and the material composition variation has an important effect on structural wave propagation behavior.