Analysis of Wave Propagation in Functionally Graded Material Annular Sector Plates Using Curved-Boundary Legendre Spectral Finite Elements

Abstract

Functionally graded materials (FGMs) are a kind of composite materials, where its properties change along spatial coordinates. Study on wave propagation in the FGMs is for the detection of damage. A time-domain 2D curved edge spectral finite element method (SFEM) is introduced in this paper to model wave propagation in complex FGM structures. According to the classic finite method, the shape functions of SFEM uses the Lagrange interpolation polynomials at Gauss-Lobatto-Legendre (GLL) points. GLL quadrature rules are used to calculate the element matrix, which brings the advantage of diagonal mass matrix. In addition to beyond that, the spatial variation of material properties inside the element is under considerations and the quadratic Lagrange polynomial as interpolation functions can represent the curved boundary of structure. The efficiency of the introduced SFEM model simulating lamb wave propagation in FGM rectangle plates is illustrated and verified by analytical data. The wave responses in a FGM ring are solved by straight edge SFEs and curved edge SFEs respectively to prove the efficiency of the curved edge element. Finally, wave propagation in the FGM ring is studied through the vibration mode, time domain response and phase velocity. Also, the effects of excitation frequency and FGM parameters are investigated. The results demonstrate that the developed curved edge SFEs and SFEM model can offer an efficient and realistic simulation for wave propagation in two-dimensional FGM structures with curved edge.