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The dispersion behavior of waves in a layered magneto-electro-elastic plate is studied. Formulations are given for open-circuit surface and short-circuit surface, respectively. Legendre orthogonal polynomial series approach is employed to solve the coupling magneto-electro-elastic controlling equations. The obtained dispersion curves for the open-circuit surface are compared with the published data to confirm the validity of the method. Through numerical examples, the convergence of the method is discussed. The differences of the two boundaries are illustrated. The influences of the piezoelectricity and piezomagnetism are illustrated and the influential factors of the piezoelectric and piezomagnetic effect are discussed. Finally, the influences of the volume fraction and stacking sequence on the piezoelectric effect and piezomagnetic effect are discussed.

In this paper, viscoelastic shear horizontal (SH) wave propagation in functionally graded material (FGM) plates and laminated plates are investigated. The controlling differential equation in terms of displacements is deduced based on the Kelvin–Voigt viscoelastic theory. The SH wave characteristics is controlled by two elastic constants and their corresponding viscous coefficients. By the Legendre polynomial series method, the asymptotic solutions are obtained. In order to verify the validity of the method, a homogeneous plate is calculated to make a comparison with available data. Through three different graded plates, the influences of gradient shapes on dispersion and attenuation are discussed. The viscous effects on the displacement and stress shapes are illustrated. The different boundary conditions are analyzed. The influential factors of the viscous effect are analyzed. Finally, two multilayered (two layer and five layer) viscoelastic plates that are composed of the same material volume fraction are calculated to show their differences from the graded plate.

Piezoelectric-piezomagnetic functionally graded materials (FGM), with a gradual change of the mechanical, electric and magnetic properties, have great promise for different applications. Based on the Legendre orthogonal polynomial series expansion approach, a dynamic solution is presented for the propagation of harmonic waves in piezoelectric-piezomagnetic FGM spherical curved plates. The material properties are assumed to vary in the direction of the thickness according to a known variation law. The dispersion curves of the piezoelectric-piezomagnetic FGM spherical curved plate and the corresponding non-piezoelectric, non-piezomagnetic plates are calculated to show the influences of the piezoelectricity and piezomagnetism. Electric potential and magnetic potential distributions are also obtained to illustrate the different influences of the piezoelectricity and piezomagnetism. Finally, a spherical curved plate at different ratio of radius to thickness is calculated to show the influence f the ratio on th...

In this article, the propagation of guided thermoelastic waves in the circumferential direction of orthotropic cylindrical curved plates subjected to stress-free, isothermal boundary conditions is investigated in the context of the Green-Naghdi (GN) generalized thermoelastic theory (without energy dissipation). The coupled wave equations and heat conduction equation are solved by the Legendre orthogonal polynomial series expansion approach. The convergency of the method is discussed through a numerical example. The dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Dispersion curves of the corresponding pure elastic cylindrical plate are also shown to analyze the influence of the thermoelasticity on elastic modes. The displacement, temperature and stress distributions are shown to discuss the differences between the elastic modes and thermal modes. A thermoelastic cylindrical plate with a different ratio of radius to thickness is considered to discuss the influence of the ratio on the characteristics of circumferential thermoelastic waves.

In this article, the propagation of thermoelastic waves in orthotropic spherical curved plates subjected to stress-free, isothermal boundary conditions is investigated in the context of the Green–Naghdi (GN) generalized thermoelastic theory (without energy dissipation). The theoretical formulation is based on the linear GN thermoelastic theory. The coupled wave equation and heat conduction equation expressed by the displacement and temperature are obtained. By the Legendre orthogonal polynomial series expansion approach, the coupled controlling equations are solved. The convergence of the method is demonstrated through a numerical example. The dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Dispersion curves of the corresponding purely elastic spherical plate are also shown to analyze the influence of thermoelasticity on elastic modes. The displacement, temperature and stress distributions of both elastic modes and thermal modes are calculated to show their differences. A thermoelastic spherical plate with a different ratio of radius to thickness is considered to show the influence of the ratio on the characteristics of thermoelastic waves.

A dynamic solution is presented for the propagation of harmonic waves in imhomogeneous (functionally graded) magneto-electro-elastic plates composed of piezoelectric BaTiO3 and magnetostrictive CoFe2O4. The materials properties are assumed to vary in the direction of the thickness according to a known variation law. The Legendre orthogonal polynomial series expansion approach is employed to determine the wave propagating characteristics in the plates. The dispersion curves of the imhomogeneous piezoelectric–piezomagnetic plate and the corresponding non-piezoelectric, non-piezomagnetic plates are calculated to show the influences of the piezoelectricity and piezomagnetism on the dispersion curves. They are compared with the dispersion curves of the plates with the different magnetic constants to illustrate the influential factors of the piezoelectric and piezomagnetic effect for the wave propagation in a magneto-electro-elastic plate. Electric potential and magnetic potential distributions at different wavenumbers are also obtained to illustrate the different influences of the piezoelectricity and piezomagnetism.

Based on linear three-dimensional piezoelasticity, the Legendre orthogonal polynomial series expansion approach is used for determining the wave characteristics in hollow cylinders composed of the functionally graded piezoelectric materials (FGPM) with open circuit. The displacement and electric potential components, expanded in a series of Legendre polynomials, are introduced into the governing equations along with position-dependent material constants so that the solution of the wave equation is reduced to an eigenvalue problem. Dispersion curves for FGPM and the corresponding non-piezoelectric hollow cylinders are calculated to show the piezoelectric effect. The influence of the ratio of radius to thickness is discussed. Electric potential and displacement distributions are used to show the piezoelectric effect on the flexural torsional mode. The influence of the polarizing direction on the piezoelectric effect is illustrated. For the radial and axial polarization, the piezoelectric effect reacts mostly on the longitudinal mode. For circumferential polarization, the piezoelectric effect reacts mostly on the torsional mode. In the FGPM hollow cylinder, piezoelectricity can weaken the guided wave dispersion.

Functionally graded piezoelectric material (FGPM), with a gradual change of the mechanical and electric properties, has large fields of application. Based on linear three-dimensional piezoelasticity, a Legendre orthogonal polynomial series expansion approach is used for determining the characteristics of circumferential waves in FGPM cylindrical curved plates. Our results from an FGPM cylindrical curved plate with a large ratio of radius to thickness are compared with an FGPM flat plate published earlier to confirm the accuracy and range of applicability of the computational program. Circumferential wave dispersion curves for FGPM and the corresponding FGM cylindrical curved plates are calculated and the effect of piezoelectricity is shown. The influence of the ratio of radius to thickness on the piezoelectric effect and electric potential distribution is discussed. The ratio has a significant influence on the electric potential distribution. Finally, the influence of the polarizing direction on the piezoelectric effect is illustrated. The phenomenon that piezoelectricity weakens the guided wave dispersion in the FGPM cylindrical plate is observed.

Based on linear three-dimensional piezoelasticity, a Legendre orthogonal polynomial series expansion approach is used for determining the characteristics of guided waves in continuous functionally graded piezoelectric materials (FGPM) as spherically curved plates. The displacement components and electric potential, expanded in a series of Legendre polynomials, are introduced into the governing equations along with position-dependent material constants so that the solution of the wave equation is reduced to an eigenvalue problem. Our results from a homogeneous anisotropic spherically curved plate are compared with those published earlier to confirm the accuracy and range of applicability of this polynomial approach. Guided-wave dispersion curves for FGPM and the corresponding FGM spherically curved plates are calculated and the effect of piezoelectricity is shown. The mechanical displacement distribution and electric potential distribution are also illustrated. Finally, the influence of the ratio of radius to thickness on the dispersion curves is discussed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In ultrasonic nondestructive inspection of large-diameter pipes and curved plate, longitudinal cracks are detected more efficiently by using guided circumferential waves. In the present, the study of guided circumferential waves and their application in detecting longitudinal defect were relative adequate when pipe material is isotropic. Based on linear three-dimensional elasticity, an orthogonal polynomial series expansions approach is used for determining the guided circumferential waves dispersion curves in homogeneous infinitely long orthotropic hollow cylinders. Results are compared with those published earlier and with the finite element simulation to check up the accuracy and range of applicability of this polynomial approach. Through the analysis of the displacements distributions and finite element simulation, the mode conversion of guided circumferential waves by end-reflection in cylindrical curved plate is discovered.

For ultrasonic non-destructive inspection of spherical curved plates, which is used in the fields of pressure vessels, spherical domes of power plants, and so on, characteristics of guided waves in spherical curved plates must be understood. Based on linear three-dimensional elasticity, an orthogonal polynomial series expansion approach is used for determining the guided wave dispersion curves and the displacements distributions in homogeneous anisotropic spherical curved plates. When the material is orthotropic or has fewer independent constants in the wave propagation direction, the coupled propagating waves can be decomposed of Lamb-like waves and SH wave. The independent SH wave is solved analytically by Bessel function. In order to test the accuracy and range of applicability of this polynomial approach, the two results of the SH wave is compared, the exact results by Bessel function and the results by the polynomial method. Guided wave dispersion curves for unidirectional composite spherical curved plates with different fiber intensity are calculated to show the effect of the fiber intensity on dispersion curves. Finally, the guided wave dispersion curves for orthotropic spherical curved plates at different radius of curvature are calculated and the inherited influences of the radius of curvature on the wave characteristics are discussed.