Time-harmonic loading over a piezoelectric layered half-space

Abstract

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.