The complex Rayleigh waves play an important role in the energy conversion efficiency of magneto-electro-elastic devices, so it is necessary to explore the wave propagation characteristics for the better applications in engineering. This paper modifies the Laguerre orthogonal polynomial to investigate the complex Rayleigh waves propagating in nonhomogeneous magneto-electro-elastic half-spaces. The improved method simplifies the calculation process by incorporating boundary conditions into the constitutive relations, shortens the solving time by transforming the solution of wave equation to an eigenvalue problem, and obtains all wave modes, including real and imaginary and complex wavenumbers. The three-dimensional curves of full frequency spectrum and phase velocities are presented for the better description of the conversion from complex Rayleigh wave modes to real wave ones; besides, the displacement distributions, electric and magnetic potential curves are obtained in thickness and propagation directions, respectively. Numerical results are analyzed and discussed elaborately in three cases: variation of nonhomogeneous coefficients, absence of magnetism, and absence of electricity. The results can be used to optimize and fabricate the acoustic surface wave devices of the nonhomogeneous magneto-electro-elastic materials.

The research on the propagation of surface waves has received considerable attention in order to improve the efficiency and natural life of the surface acoustic wave devices, but the investigation on complex Rayleigh waves in functionally graded piezoelectric material (FGPM) is quite limited. In this paper, an improved Laguerre orthogonal function technique is presented to solve the problem of the complex Rayleigh waves in an FGPM half-space, which can obtain not only the solution of purely real values but also that of purely imaginary and complex values. The three-dimensional dispersion curves are generated in complex space to explore the influence of the gradient coefficients. The displacement amplitude distributions are plotted to investigate the conversion process from complex wave mode to propagating wave mode. Finally, the curves of phase velocity to the ratio of wave loss decrements are illustrated, which offers extra convenience for finding the high phase velocity points where the complex wave loss is near zero.

Due to mechanical loads, thermal fields and the limitation of the manufacturing technology, initial stresses in layered cylindrical structures are ineluctable. Accordingly, for the purpose of the guided wave nondestructive testing for the layered cylindrical structure with a sectorial cross-section, an analytical approach, the double-orthogonal polynomial method is utilized to investigate the influence of axial initial stress on wave characteristics. Based on Biot’s “Mechanics of Incremental Deformations”, the dynamic equations for the sectorial cylindrical structures in terms of displacements and axial initial stress are deduced. By virtual of the Heaviside function, the boundary conditions are automatically incorporated into constitutive equations and then into wave equations. The corresponding dispersion curves and displacement distributions of various sectorial cylindrical structures are calculated. Numerical results indicate that the influence of the initial stress applied on the outer layer is much significant at low frequencies, and the influence of the initial stress applied on the inner layer is much significant at high frequencies; the cut-off frequencies have negative relation with the area of the cross-section; the displacements at high frequencies are mainly distributed in the layer with smaller elasticity modulus, especially the layer simultaneously with bigger initial stress.