Building upon our previous work, this paper presents a two-dimensional (2D) modeling of a transverse-type rectangular piezoelectric transformer with common ground electrodes based on the Legendre Polynomial Approach (LPA), under the plane stress assumption and without neglecting the length between the primary and secondary electrodes called gap. Aiming to confirm the validated previous theoretical predictions obtained via PZT-5A ceramic, the studied device was designed, realized, and characterized from lead-free ceramic by selecting Barium Titanate (BaTiO or BT, belonging to the 4mm crystallographic point group of the tetragonal system) film in compliance with the European directive on lead (Pb) usage. Problem resolution via LPA lies in the formulation of mechanical displacement and electric potential, expanded in each region as a series of orthonormal Legendre polynomials with appropriate expressions, specifically constructed to satisfy boundary and continuity conditions, which are directly incorporated into the propagation equations through the delta function. Then, analytical results are modeled numerically using Matlab software. In addition, a three-dimensional (3D) numerical simulation of the same structure was performed by applying the Finite Element Model (FEM) using Comsol Multiphysics software. Electrical and mechanical responses were obtained. Results found from both FEM and LPA strongly match the experimental data. Finally, the proposed method enabled the detailed study, analysis, and optimization of all physical quantities and parameters within this electromechanical device, for improving its performance.

Our paper focuses on wave propagation in a circular annular piezoelectric plate with hexagonal elastic symmetry used in Micro-Electromechanical Systems (MEMS). The objective is to examine the properties of two piezoelectric materials: PZT-5A, a soft ceramic used in ultrasonic sensors, and PZT-4, a strong ceramic used in ultrasonic actuators. We developed the Legendre orthogonal polynomial method to obtain semi-analytical solutions for the governing equations. One strength of our method is that it can analyze the global structure using a single formalism calculation. The analysis takes into consideration the alternating current excitation and directly includes the boundary conditions into the vibration equations. As a result, we found that the limit value of voltage across the electrodes equals that can be applied to determine the maximum von Mises stress without exceeding the yield stress value of for the PZT4. The electromechanical coupling coefficient shows that the fundamental mode is the most piezoactive mode in the structure. Furthermore, we present the natural frequencies, electrical input impedance, field profiles, and dispersion curves. To validate the efficiency and accuracy of our approach, we compared our results with those obtained using voltage excitation and analytical data. Ultimately, we achieved a good agreement between them.

The semi-analytical modeling of acoustic wave resonators is discussed in this study. A polynomial approach to wave propagation is used to predict the electromechanical behavior of piezoelectric resonators in a circular ring with hexagonal elastic symmetry. We present a Legendre polynomial-based 3D semi-analytical technique capable of accounting for finite lateral dimensions. Using delta functions, the boundary conditions are immediately integrated into the wave equations. The Legendre polynomial method’s validity is confirmed by comparing polynomial results with finite element method (FEM) results from the literature.

This paper presents an application of Legendre polynomial approach to solve the wave propagation in a piezoelectric ZnO planar resonator subjected to stress-free boundary conditions and excited using two thin electrodes connected to an electrical source. The method is able to take into account the boundary conditions, the presence of electrical source and the different dissimilarities of the physical properties. Resonance frequencies of longitudinal modes are calculated in case of an open and short-circuit brunch. Dispersion characteristics are also calculated such as mechanical displacement and stress profiles for different resonance frequencies. The electromechanical coupling coefficient is also calculated.

This article presents an extension of the double Legendre polynomial method to model and evaluate the axisymmetric free vibration problem for the axially polarized piezoelectric resonator. The aim is to show the benefit of the employed method. The polynomial series was used to define the mechanical displacements and electrical potential at the same time. The proposed approach considerably improves computing efficiency by avoiding much of the numerical integration calculations. As a result, the electromechanical coupling coefficient shows that the fundamental mode is the most piezoactive mode in the structure. Furthermore, the electrical input impedance and field profiles are easily presented.

A polynomial approach is used for solving wave propagation to forecast the performance of piezoelectric transformers (PTs). The method consists in integrating straightforwardly into the equation of motion via a delta function the continuity and boundary conditions. Resonance and anti-resonance frequencies, electrical and acoustical fields of the PTs are obtained. The energy harvest in the piezoelectric transformer is presented. The validation of the model is done through a comparison of our results against the 2D Finite Element Method ones.

A Legendre polynomial approach (PA) is proposed to forecast a thin film of transverse-type rectangular piezoelectric transformer (PT) performance with common ground electrodes located on its whole bottom surface, fabricated from a PZT5A (lead zirconate titanate) ceramic material. Based on the automatic incorporation of boundary conditions into the equations of motion and the development on a basis of orthonormal polynomials of the fields, formulations calculated analytically are simulated numerically. Then, series and parallel resonance frequencies, profiles of the mechanical displacement and the electrical potential are obtained for the PT. Our results are validated through a comparison with the three-dimensional Finite Element Method (FEM) ones. Furthermore, the mechanical tethers positions are located at the PT’s junctions.

A 2-D semianalytical model using the Legendre polynomial approach was applied for modeling the piezoelectric transformer (PT). In the model, the mechanical displacements and the electric potential were expanded in a double series of orthonormal polynomials with an appropriate analytical form. Series and parallel resonance frequencies, input electrical admittance, and voltage gain were obtained for the PT. The results are in excellent agreement with both the numerical results calculated with a 3-D finite-element analysis and experimental ones. The approach is able to predict the behavior of a wide and a long PT.