Guided waves in multilayered hollow cylinders: The improved Legendre polynomial method

Legendre polynomial series method has been proposed to solve the wave propagation in multilayered flat plates for more than 10 years. But it has never been used for curved waveguides. This method has intrinsic limitations: it can deal only with low contrast multilayered structures and is unable to restitute correct continuous normal stress distributions. This paper proposes an improvement of the Legendre polynomial method to overcome these drawbacks and uses it to solve the guided wave propagation in general multilayered hollow cylinders i.e. with or without very dissimilar material properties. Detailed formulations are given to show the differences between the improved orthogonal polynomial method and the conventional one. Through a numerical comparison among the exact solution (from the transfer matrix method), the improved polynomial approach and the conventional polynomial approach, the validity of the improved polynomial approach is illustrated. Then, the flexural guided wave dispersion curves and stress distributions are analyzed. The influences of the flexural orders and of the radius to thickness ratio on flexural longitudinal wave and flexural torsional wave are discussed.