The dispersion of waves in ceramic-metal functionally graded cylindrical shell embedded in an elastic substrate

This work studies the waves’ dispersion behavior in a composite ceramic-metal functionally graded (FG) cylindrical shell embedded in an elastic foundation. The present developed formulation is based on the integral higher-order shear deformation shell theory which takes into account the correct distribution of the transverse shear stresses. the proposed model reduces the time and cost of calculation because to the reduced number of unknown variables compared to other existing models. The effective material properties of the composite shell are assumed to obey the mixture rule and the power-law of volume fractions. Considering a surrounding elastic medium, the set of governing equations is found by employing Hamilton’s principle within the framework of an integral higher-order shear deformation shell theory. The behaviors of the principal frequency and the phase velocity of waves propagating in the shells are investigated by considering their response due to changes in wavenumbers, material exponent, cylindrical shells’ radius-to-thickness ratio, and the two parameters of the surrounding elastic medium. The results indicate that Winkler and Pasternak's parameters significantly influence the behavior of wave propagation in thinner shells as the waves’ frequency and phase velocity increase with the increases of these two parameters. In addition to contributing to improving the design efficiency of FGM cylindrical shells, the results presented in this paper will serve as a valuable reference for future researchers.