Waves in fluid-filled functionally graded piezoelectric hollow cylinders: A restudy based on the reverberation-ray matrix formulation

A functionally graded piezoelectric hollow cylinder (or cylindrical shell) with arbitrary through-thickness variation of material properties may be approximated as a multilayered cylinder, which then can be analyzed effectively based on the state–space formulation. However, the state–space formulation is not always numerically stable. On the other hand, the reverberation-ray matrix formulation is unconditionally numerically stable, but no attempt has been made in the cylindrical coordinates with the dominant direction along the radial direction. This paper links the two formulations together with the aid of a symplectic framework. Thus, the reverberation-ray matrix formulation is properly established to analyze the wave propagation in a fluid-filled functionally graded piezoelectric hollow cylinder, along with an approximate laminate model. Results confirm that the calculation based on the developed formulation is unconditionally stable. The influence of various parameters on the dispersion behavior is also studied numerically. ► The reverberation-ray matrix formulation for cylindrical coordinates is established. ► Numerical example demonstrates the accuracy and stability of the proposed method. ► Material inhomogeneity mainly affects the wave propagation for high modes. ► Frequency is very sensitive to the velocity ratio between fluid and the cylinder.