Numerical study of S1 zero group velocity Lamb modes for nonlinear functionally graded materials

Abstract

This paper presents detailed theoretical investigation of the first-order symmetric zero group velocity (S1-ZGV) modes propagating in functionally graded material (FGM) plates. Governing equations for the Lamb waves are derived and the power series technique (PST) is employed to solve the recursive equations associated with any power law and its gradient coefficient. The convergence criteria relative to PST have been discussed. Then, the dispersion curves are obtained on the basis of PST. Additionally, the impact of the FGM base materials and the gradient coefficient on S1-ZGV frequency is investigated. Numerical results show that S1-ZGV frequency is comparatively more sensitive to the shear modulus than to the Lamé parameter λ. Additionally, the variations of S1-ZGV frequency as a function of the Poisson ratio of various FGM plates are clarified.