Lamb Waves in a Functionally Graded Composite Plate with Nonintegral Power Function Volume Fractions

Abstract

An analytical modelling is carried out to determine the Lamb wave’s propagation behavior in a thermal stress relaxation type functionally graded material (FGM) plate, which is a composite of two kinds of materials. The mechanical parameters depend on the volume fractions, which are nonintegral power functions, and the gradient coefficient is the power value. Based on the theory of elastodynamics, differential equations with variable coefficients are established. We employ variable substitution for theoretical derivations to solve the ordinary differential equations with variable coefficients using the Taylor series. The numerical results reveal that the dispersion properties in some regions are changed by the graded property, the phase velocity varies in a nonlinear manner with the gradient coefficient, nondispersion frequency exists in the first mode, and the set of cutoff frequencies is a union of two series of approximate arithmetic progressions. These results provide theoretical guidance not only for the experimental measurement of material properties but also for their nondestructive testing.