In this paper, the acoustic wave motion characteristics of Lamb and SH waves in functionally graded (FG) anisotropic micro/nano-plates are studied based on the modified couple stress theory. A higher efficient computational approach, the extended Legendre orthogonal polynomial method (LOPM) is utilized to deduce solving process. This polynomial method does not need to solve the FG micro/nano-plates hierarchically, which provides a more realistic analysis model for FG micro/nano-plates and has high computational efficiency. Simultaneously, the solutions based on the global matrix method (GMM) are also deduced to verify the correctness of the polynomial method. Furthermore, the effects of size and material gradient are studied in detail. Numerical results show that the size effect causes wrinkles in Lamb wave dispersion curves, and the material gradient characteristic changes the amplitude and range of wrinkles. For SH waves, the length scale parameter Lx increases the cut-off frequency but does not change the overall trend of the dispersion curve; on the contrary, Lz does not change the cut-off frequency but causes the dispersion curve to show an upward trend.

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Dispersion characteristics of guided waves in functionally graded anisotropic micro/nano-plates based on the modified couple stress theory

Analysis of Lamb wave propagation in a functionally graded piezoelectric small-scale plate based on the modified couple stress theory

Wave propagation in thermoelastic inhomogeneous hollow cylinders by analytical integration orthogonal polynomial approach

A nonlocal stress expansion Legendre orthogonal polynomial method is proposed to study the reflection and transmission of elastic waves through piezoelectric nanoplates sandwiched in two solid half-spaces. The proposed method avoids employing the relationship between local stress and nonlocal stress to construct boundary conditions. The reflection and transmission of plane waves and out-plane waves are studied separately with considering the electrical open circuit boundary. The convergence of presented method is discussed. The correctness of presented method is verified by comparing with the published data of piezoelectric nanoplates immersed in water, which can be considered as a simplified situation sandwiched in two solid half spaces. In addition, the nonlocal effect on the wave mode conversion, stress and electric displacement distribution, and piezoelectricity are discussed. Results show that the nonlocal effect reconstructs the wave mode conversion, and enhances the influence of the piezoelectricity on the critical angle.

Reflection and transmission of elastic waves through nonlocal piezoelectric plates sandwiched in two solid half-spaces

Mixed-dimensional 1D CdS/2D MoSe2 heterostructures for high-performance photocatalytic hydrogen production

The fractional Kelvin-Voigt model for circumferential guided waves in a viscoelastic FGM hollow cylinder

Compared to the traditional integer-order viscoelastic model, a fractional-order derivative viscoelastic model is shown to be advantageous. A quadrature-free Legendre polynomial method combining th...

Guided wave propagation in functionally graded fractional viscoelastic plates: A quadrature-free Legendre polynomial method

Functionally graded piezoelectric-piezomagnetic material (FGPPM), with a gradual variation of the material properties in the desired direction(s), can improve the conversion of energy among mechanical, electric, and magnetic fields. Full dispersion relations and wave mode shapes are vital to understanding dynamic behaviors of structures made of FGPPM. In this paper, an analytic method based on polynomial expansions is proposed to investigate the complex-valued dispersion and the evanescent Lamb wave in FGPPM plates. Comparisons with other related studies are conducted to validate the correctness of the presented method. Characteristics of the guided wave, including propagating modes and evanescent modes, in various FGPPM plates are studied, and three-dimensional full dispersion and attenuation curves are plotted to gain a deeper insight into the nature of the evanescent wave. The influences of the gradient variation on the dispersion and the magneto-electromechanical coupling factor are illustrated. The displacement amplitude and electric potential and magnetic potential distributions are also discussed in detail. The obtained numerical results could be useful to design and optimize different sensors and transducers made of smart piezoelectric and piezomagnetic materials with high performance by adjusting the gradient property.

The Computation of Complex Dispersion and Properties of Evanescent Lamb Wave in Functionally Graded Piezoelectric-Piezomagnetic Plates

Each guided elastic wave mode is composed of propagating and non-propagating branches. Non-propagating branches associated with complex wavenumbers are substantially different from the propagating ...

https://journals.sagepub.com/doi/pdf/10.1177/1687814019836878

Zhi Li

Papers

The fractional Kelvin-Voigt model for circumferential guided waves in a viscoelastic FGM hollow cylinder

Guided wave propagation in functionally graded fractional viscoelastic plates: A quadrature-free Legendre polynomial method

The Computation of Complex Dispersion and Properties of Evanescent Lamb Wave in Functionally Graded Piezoelectric-Piezomagnetic Plates

Properties of circumferential non-propagating waves in functionally graded piezoelectric cylindrical shells:

Circumferential thermoelastic Lamb wave in fractional order cylindrical plates