Xiaoming Zhang

Piezoelectric nanoplates play a crucial role in Micro/Nanoelectromechanical systems (MEMS/NEMS), yet their vibration behavior is significantly influenced by size effects at the nanoscale. Traditional 2D nanoplate models have limitations in predicting complex stress–strain distributions and higher-order modes due to simplifying assumptions regarding the thickness direction. This paper establishes an electromechanical coupling vibration model for piezoelectric rectangular nanoplates by integrating Eringen’s nonlocal theory with 3D elasticity theory. The complex 3D partial differential equations are transformed into a matrix eigenvalue problem by employing the analytically integrated triple Legendre polynomial expansion method, yielding series solutions for the natural frequencies and modal fields. The validity of the proposed method is verified against existing data in the literature, followed by a discussion on convergence and computational efficiency. The influences of the nonlocal effect, piezoelectric effect, boundary conditions, and geometric properties on the vibration characteristics of piezoelectric nanoplates are investigated in detail. Compared with the finite element method or meshless methods, the proposed method provides analytical solutions based on series expansion, which can reveal the effects of system parameters on vibration behavior more deeply, offering theoretical guidance for the design of NEMS devices.

Purpose: This study aims to investigate non-Fourier heat transfer in multilayer biological tissues subjected to laser irradiation and to develop a machine learning-based surrogate framework for rapid and accurate prediction of tissue temperature. Design/methodology/approach: A three-layer skin model consisting of the epidermis, dermis and subcutaneous tissue is developed by combining wavelength-dependent optical absorption based on the Beer–Lambert law with the Green-Naghdi non-Fourier heat conduction theory. The governing equations are solved numerically using an implicit finite difference method. Artificial Neural Network and XGBoost models are trained to predict the temperature field from the numerical data. Findings: The results demonstrate that wavelength-dependent laser absorption and finite-speed heat conduction significantly influence the thermal response of skin tissues. A transition from surface-dominated to subsurface heating is observed, leading to nonlinear thermal safety boundaries. Among the surrogate models, XGBoost achieves excellent prediction accuracy (R2 > 0.99) while considerably reducing computational time compared with the numerical model. Originality/value: The study integrates a non-Fourier bioheat transfer model with machine learning-based surrogate prediction to provide an efficient framework for rapid thermal analysis of laser-irradiated multilayer skin tissues, offering potential applications in laser therapy planning, treatment optimization and real-time thermal monitoring.

This study presents an analytical and data-driven investigation of shear-horizontal (SH) wave propagation in layered piezo-flexoelectric (PFE) materials with imperfect interfaces. The novelty lies in integrating flexoelectric coupling and interfacial defects within a unified dispersion framework, supported by physics-consistent machine-learning surrogates for efficient parametric analysis. Governing electromechanical equations are formulated and solved under mechanical, electrical, and interfacial continuity conditions to derive dispersion relations linking phase velocity with wavenumber, flexoelectric parameters, and interface stiffness under electrically open and short-circuited boundary conditions. The results show that flexoelectric effects strongly influence dispersion at short wavelengths, while interface imperfections significantly reduce phase velocity and increase attenuation sensitivity. Electrically open conditions enhance electromechanical coupling, whereas short-circuit conditions suppress dispersion sensitivity. To accelerate large-scale evaluations, surrogate models are developed that accurately reproduce analytical dispersion behavior with substantially reduced computational cost. The proposed hybrid framework provides improved insight into guided wave mechanics in stratified smart materials and offers an efficient tool for the analysis and design of piezo-flexoelectric structures in sensing and MEMS applications.

For the purpose of design and optimization for piezoelectric quasi-crystal transducers, guided waves in a functionally graded 1-D hexagonal piezoelectric quasi-crystal plate are investigated. In this paper, a model combined with the Bak’s and elastohydrodynamic models is utilized to derive governing equations of wave motion, and real, pure imaginary, and complex roots of governing equations are calculated by using the modified Legendre polynomial method. Subsequently, dispersion curves and displacements of phonon and phason modes are illustrated. Then, guided waves in functionally graded 1-D hexagonal piezoelectric quasi-crystal plates with different quasi-periodic directions are studied. And the phonon-phason coupling effect on Lamb and SH waves are analyzed. Accordingly, some interesting results are obtained: The phonon-phason coupling just affects Lamb waves in the x - and z -direction quasi-crystal plates, and SH waves in the y -direction quasi-crystal plate. Besides, frequencies of propagative phason modes decrease as phonon-phason coupling coefficients R _i increase. Furthermore, a variation in the polarization has a more significant influence on phonon modes, and a variation in the quasi-periodic direction has a more significant influence on phason modes.

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.

The improvement of the resolution and energy conversion efficiency of piezoelectric devices requires a thorough study of guided wave, especially the evanescent wave modes with high-phase speed and low attenuation. Due to the computation difficulties, investigations about the evanescent wave in piezoelectric structures are rather limited. In this article, an analytic method based on the orthogonal function technique is presented to investigate the complex dispersion relations and the evanescent guided wave in functionally graded piezoelectric plates, which can convert the complex partial differential equations with variable coefficients into an eigenvalue problem and obtain all solutions. Comparisons with other related studies are conducted to validate the correctness of the presented method. Three-dimensional full dispersion curves are plotted to gain a better insight into the nature of the evanescent waves. The influences of piezoelectricity and graded fields and electrical boundary conditions on evanescent waves are illustrated. The electromechanical coupling factors of the functionally graded piezoelectric material plates with different gradient fields are also investigated. Furthermore, the displacement amplitude and electric potential distributions are also discussed to illustrate the specificities of evanescent guided waves. The corresponding results presented in this work are promised to be used to improve the resolution of piezoelectric transducers.

The vibration modes of an elastic plate are usually divided into propagating and non-propagating (evanescent) kinds. Non-propagating wave modes are very important for guided wave inspection of defect size and shape. But it is difficult to obtain the complex solutions of the transcendental dispersion equation, corresponding to the non-propagating wave. In this article, we present an improved Legendre polynomial method to calculate the complex-valued dispersion and study properties of the non-propagating wave in a piezoelectric spherical plate. Comparisons with other related studies are conducted to validate the correctness of the presented method. The complete dispersion and attenuation curves are plotted in three-dimensional frequency-complex wave number space. The influences of material piezoelectricity and radius–thickness ratio on non-propagating waves in piezoelectric spherical plates are investigated. The amplitude distributions of the electric potential and displacement are also discussed in detail. All the results presented in this work can provide theoretical guidance for ultrasonic nondestructive evaluation and are promising to be applied to improve the resolution of piezoelectric transducers.