A novel local radial basis function collocation method for multi-dimensional piezoelectric problems

The local radial basis function collocation method (LRBFCM), a strong-form formulation of the meshless numerical method, is proposed for solving piezoelectric medium problems. The proposed numerical algorithm is based on the local Kansa method using variable shape parameter. We introduce a novel technique for the determination of shape parameter in the LRBFCM, which leads to greater accuracy, and simplicity. The implemented algorithm is first verified with a 2D Poisson equation. Then, we employed LRBFCM in a numerical simulation for 2D and 3D piezoelectric problems involving mutual coupling of the electric field and elastodynamic equations for mechanical field. The presented meshless method is verified using corresponding results obtained from the finite element method and moving least squares meshless local Petrov–Galerkin method. In particular, the 2D piezoelectric problem is verified with an exact solution.

Numerical investigation of the effects of partial metallization at the pore surface on the effective properties of a porous piezoceramic composite

This paper presents a numerical homogenization analysis of a porous piezoelectric composite with a partially metalized pore surface. The metal layers can be added to the pore surfaces to improve the mechanical and electromechanical properties of ordinary porous piezocomposites. Physically, constructing that composite with completely metalized pore surfaces is a challenging process, and imperfect metallization is more expected. Here, we investigate the effects of possible incomplete metallization of pore surfaces on the composite’s equivalent properties. We applied the effective moduli theory, which was developed for the piezoelectric medium based on the Hill–Mandel principle, and the finite element method to compute the effective moduli of the considered composites. Using specific algorithms and programs in the ANSYS APDL programming language, we constructed the representative unit cell element models and performed various computational experiments. Due to the presence of metal inclusion, we found that the dielectric and piezoelectric properties of the considered composites differ dramatically from the corresponding properties of the ordinary porous piezocomposites. The results of this work showed that piezocomposites with partially metallized pore surfaces can have a higher anisotropy, compared to the pure piezoceramic matrix, due to the defects in metal coatings.

Generalized Thermopiezoelectricity with Memory-Dependent Derivative and Transient Thermoelectromechanical Responses Analysis

In this paper, a novel generalized thermoelastopiezoelectric model is established by introducing memory-dependent derivative, which might be superior to fractional ones: the form is unique, while the fractional-order theories have various expressions with different authors; it is more intuitionistic for reflecting the memory effect; the physical meanings of the related memory-dependent differential equations are more clear, which are determined by the essence of their definitions; the time-delay and kernel function can be chosen freely based on the necessity of practical applications. The newly constructed model is applied to the transient shock analysis for piezoelectric medium under heating loads. Laplace transformation techniques are employed to solve the governing equations. In numerical implementation, the problem of a semi-infinite piezoelectric medium is considered under the two different cases. The transient responses, that is, temperature, displacement, stress, and electric potential, are illustrated graphically. The parametric studies are performed to analyze the effects of time-delay and kernel function on the transient thermoelastopiezoelectric responses. This work may provide a new approach to explore the transient responses’ behavior for piezoelectric materials serving in nonisothermal environment.

Model of transverse-transverse type piezoelectric transformer

The mathematical model of a piezoelectric transformer of the transverse-transverse type and describes the method of its construction has been presented. Although mathematical modeling programs for piezoelectric devices can achieve any predetermined modeling accuracy, the simulation results cannot be directly used in the development of electronic equipment, because the programs are not integrated with CADs, for this reason most often in calculations and in modeling circuits based on piezotransformers, the simplest equivalent circuit is used. But its adequately reflects currents and voltages in the piezotransformer circuit only in the vicinity of the operating resonant frequency. The proposed model is based on a one-dimensional approximation of the equations of state and dynamics of the piezoelectric medium for flat plates of constant thickness and width, which is obtained from a three-dimensional system of equations by averaging the width and thickness. While the usual approximate model often allows to model a piezotransformer with two pairs of electrodes and only in the vicinity of one resonant frequency, the model constructed in the article allows to take into account the presence of several electrodes on piezotransformer surfaces and their different relative positions on the upper and lower surfaces. 'esoplastin. Compared with the usual, the proposed model is more convenient for modeling by means of circuit modeling systems. In the developed model, the piezotransformer is represented as a set of interconnected sections that carry one pair or several pairs of electrodes on the surfaces. Also, in contrast to the usual, the proposed model allows to take into account the presence of several resonant frequencies of the piezotransformer, which allows more adequate modeling of electronic equipment that uses in its structure a piezoelectric transformer of the transverse type. On the basis of the mathematical model the scheme of substitution of separate sections of the piezoelectric transformer is constructed and formulas for calculation of parameters of elements of the scheme are given. In in the article as example the implementation of the developed model in the computer-aided design system MicroCAP has been showed.

Functionally Graded Piezoelectric Medium Exposed to a Movable Heat Flow Based on a Heat Equation with a Memory-Dependent Derivative

The current work deals with the study of a thermo-piezoelectric modified model in the context of generalized heat conduction with a memory-dependent derivative. The investigations of the limited-length piezoelectric functionally graded (FGPM) rod have been considered based on the presented model. It is assumed that the specific heat and density are constant for simplicity while the other physical properties of the FGPM rod are assumed to vary exponentially through the length. The FGPM rod is subject to a moving heat source along the axial direction and is fixed to zero voltage at both ends. Using the Laplace transform, the governing partial differential equations have been converted to the space-domain, and then solved analytically to obtain the distributions of the field quantities. Numerical computations are shown graphically to verify the effect of memory presence, graded material properties, time-delay, Kernel function, and the thermo-piezoelectric response on the physical fields.