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Magneto-electro-elastic (MEE) materials are a specific class of advanced smart materials that simultaneously manifest the coupling behavior under electric, magnetic, and mechanical loads. This unique combination of properties allows MEE materials to respond to mechanical, electric, and magnetic stimuli, making them versatile for various applications. This paper investigates the static and time-harmonic field solutions induced by the surface load in a three-dimensional (3D) multilayered transversally isotropic (TI) linear MEE layered solid. Green's functions corresponding to the applied uniform load (in both horizontal and vertical directions) are derived using the Fourier-Bessel series (FBS) system of vector functions. By virtue of this FBS method, two sets of first-order ordinary differential equations (i.e., N-type and LM-type) are obtained, with the expansion coefficients being Love numbers. It is noted that the LM-type system corresponds to the MEE-coupled P-, SV-, and Rayleigh waves, while the N-type corresponds to the purely elastic SH- and Love waves. By applying the continuity conditions across interfaces, the solutions for each layer of the structure (from the bottom to the top) are derived using the dual-variable and position (DVP) method. This method (i.e., DVP) is unconditionally stable when propagating solutions through different layers. Numerical examples illustrate the impact of load types, layering, and frequency on the response of the structure, as well as the accuracy and convergence of the proposed approach. The numerical results are useful in designing smart devices made of MEE solids, which are applicable to engineering fields like renewable energy. [ABSTRACT FROM AUTHOR]

Mathematical modeling of multilayered piezoelectric (PE) ceramic substantially acquires attention due to its distinctive advantages of fast response time, positioning, optical systems, vibration feedback, and sensors, such as deformation and vibration control. As such, fundamental solution of a PE structure is essential. This paper presents three-dimensional (3D) static and dynamic solutions (i.e. Green's functions) in a multilayered transversally isotropic (TI) PE layered half-space. The uniform vertical mechanical load, vertical electrical displacement, and horizontal mechanical load are applied on the surface of the structure. The novel Fourier-Bessel series (FBS) system of vector functions (which is computationally more powerful and streamlined) and the dual-variable and position (DVP) method are employed to solve the related boundary-value problem. Two systems of first-order ordinary differential equations (i.e. the LM- and N-types) are obtained in terms of the FBS system of vector functions, with these expansion coefficients being the Love numbers. A recursive relation for the expansion coefficients is established by using DVP method that facilitates the combination of two neighboring layers into a new one and minimizes the computational effort to a great extent. The corresponding physical-domain solutions are acquired by applying the appropriate boundary/interface conditions. Several numerical examples pertaining to static and dynamic response are solved, and the efficiency and accuracy of the proposed solutions are validated with the existing results for the reduced cases. The solutions provided could be beneficial to better developments of PE materials, configurations, fabrication, and applications in the future. [ABSTRACT FROM AUTHOR]

We present a novel approach for deriving and modeling air-coupled surface waves with applications in non-contact non-destructive testing (NDT). It is based on the fast Fourier-Bessel series system in conjunction with the unconditionally stable dual-variable and position matrix method. Parametric studies, including sensitivity analysis, are conducted to assess the feasibility of using non-contact air-coupled measurements for pavement testing, focusing on Green's functions, time-domain waveforms, and experimental frequency-velocity spectra (FVS, i.e., the estimated Green's functions from acquired truncated wavefield). The predicted experimental FVS presented in this study are synthetic dispersion images, which are distinguished from the measured experimental FVS (i.e., measured dispersion images from multichannel analysis of surface wave (MASW) test). With the derived complete solution of air-coupled dynamic responses, we find that: (1) Striking similarities between the theoretical Green's functions of vertical displacement (on the pavement surface) and pressure (in the air), as well as in their corresponding experimental FVS. (2) The proposed accurate and efficient full-wave modeling of air-coupled surface waves avoids the need for good contact between geophones/accelerometers and pavement surface. This facilitates direct inversion of shear wave velocity profiles by fitting the predicted experimental FVS to the measured one. (3) Sensitivity analysis demonstrates no significant loss of information in the pressure measured in the air, supporting the feasibility of using non-contact measurement for non-destructive testing. These results suggest that non-contact air-coupled measurements hold great promise as a viable alternative to contact measurements in non-destructive testing. • Novel air-coupled full-wavefield modeling for surface wave testing by fast FBS and unconditional DVP matrix methods. • Pressure response in air found similar to vertical displacement on solid surface. • Enable Full-wavefield inversion without direct contact to pavement surface. • No apparent loss of deeper information in air-coupled measurements from sensitivity analysis. [ABSTRACT FROM AUTHOR]

In this paper, we first derive the dynamic solution in a transversely isotropic (TI) elastic and layered half-space, induced by a time-harmonic vertical load on its surface. The solution is obtained via the efficient and unconditionally stable dual variable and position (DVP) matrix method along with the fast Fourier-Bessel series (FBS) expansion approach. In order to study the effect of material anisotropy, the degree of anisotropy, namely the ratio of the horizontal Young's modulus over vertical Young's modulus, is introduced as the key parameter, with a very reasonable assumption on other involved elastic constants in the layered TI half-space. This enables us to investigate the effect of material anisotropy on the wave Green's functions, dispersion curves, ellipticity, and polarity. By comparing with the effect of Poisson's ratio in the corresponding layered isotropic (ISO) half-space, we observe that nearly all the wave features with varying degrees of anisotropy in the TI layered half-space are similar to those with varying Poisson's ratio in the corresponding ISO half-space. This indicates the challenge or non-uniqueness in the inversion of TI velocity profiles using vertical surface loading only. • Unconditionally stable DVP matrix method is combined with the fast Fourier-Bessel series expansion. • Wave characteristics are comprehensively examined in terms of Green's function, waveforms, ellipticity, and polarity. • A more reasonable assumption of independent TI elastic constants is proposed to better represent the degree of anisotropy. • Degree of anisotropy is found to have similar effect on all aspects of wave characteristics as Poisson's ratio. [ABSTRACT FROM AUTHOR]