Complex guided waves in functionally graded piezoelectric cylindrical structures with sectorial cross-section

Abstract

For the purpose of the design and optimization of piezoelectric transducers, the modified double orthogonal polynomial series method is proposed to investigate guided waves in functionally graded piezoelectric(FGP) cylindrical structures with sectorial cross-section. The real, imaginary and complex solutions are obtained simultaneously without iterative process. The real solutions represent propagative waves; the imaginary and complex solutions are evanescent waves. The boundary conditions are incorporated into the constitutive equations by virtue of the Heaviside function. Subsequently, the amplitudes are expanded into the double orthogonal polynomial series, and the motion equations are converted into a matrix eigenvalue problem about complex wavenumber. Numerical comparison with available reference result confirms the validity of the present method. Dispersion curves and the Poynting vector distributions are illustrated. The influences of angular measure, radius-thickness ratio and graded index on dispersion curves are analyzed. Results show that there exist some evanescent guided wave modes that have higher velocities than that of the propagative wave modes and simultaneously have low attenuation at high frequencies. These results can be utilized to improve the performance of transducers.