Nonlocal Piezoelectricity Research Articles

Studies of a new-style resonator to control electro-mechanical coupling bandgap of a locally resonant piezoelectric/elastic phononic crystal double-layer nonlocal nanobeam

The paper proposed a model of a locally resonant (LR) piezoelectric/elastic phononic crystal (PC) nanobeam with periodically attached “spring-mass” resonator and additional spring between upper and lower nanobeams, as well as horizontal spring between mass and foundation. Euler beam theory and nonlocal piezoelectricity theory are coupled and introduced to plane wave expansion (PWE) method to calculate the band structures of such a model with different parameters. Numerical results and further analysis demonstrate that all the bands of double-layer nanobeam can be divided into symmetric and antisymmetric ones. Adding additional and horizontal springs play a role in control the symmetric and antisymmetric bands respectively, which make wider band gaps be opened than corresponding single-layer nanobeam. Moreover, the change of parameters of electro-mechanical coupling fields and resonator can be applied to effectively control the starting frequencies and widths of band gaps, which can provide a theoretical basis for active control of vibration. Effects of geometric and non-dimensional nonlocal parameters on band gaps are also discussed. All the studies are expected to be applied to actively control vibration propagation in the field of nano electro-mechanical system (NEMS).

Nonlinear vibration of piezoelectric laminated nanobeams at higher modes based on nonlocal piezoelectric theory

The presented paper investigates the nonlinear vibration of a nanobeam with a piezoelectric layer bounded to its top surface considering the nonlocal piezoelectricity theory. To do this, Hamilton’s principle is implemented to derive the governing nonlinear vibration equations of the nanobeam by assumption of nonlocal piezoelectricity and a nonlinear strain–displacement relation. Then, the Galerkin separation method is applied to transform and simplify the partial differential equation of the nonlinear oscillation to an ordinary one with quadratic and cubic nonlinearities in the time domain. By implementing the multiple-scale perturbation method, an analytical relation for the nonlinear natural frequencies is obtained as a function of the oscillation amplitude and the nonlocal size scale parameter. Then, the nonlinear vibration characteristics of the nanobeam are investigated at higher modes of vibration and the size scale effects are reviewed comprehensively. It is observed that the nonlocal parameter decreases the nonlinear natural frequencies and becomes noticeable at higher modes of vibration. Moreover, by increasing the amplitude ratio, the nonlocal effects are decreased and the nonlocal nonlinear frequency approaches the local one. Also, the amplitude ratio has increasing effects on the nonlinear frequencies.

Double harmonically excited nonlinear vibration of viscoelastic piezoelectric nanoplates subjected to thermo-electro-mechanical forces

The objective of the present paper is to comprehensively study the nonlinear frequency response of viscoelastic piezoelectric nanoplates exposed to dual harmonic external excitation and thermo-electro-mechanical loads. To achieve this goal, firstly, a piezoelectric nanoplate resting on a viscoelastic foundation is modeled. Secondly, using the nonlocal piezoelectricity theory, Kelvin–Voigt model, von Karman nonlinear relations and Hamilton’s principle, the nonlinear governing differential equation of motion is derived. In the next step, employing the Galerkin technique and multiple time scales method, the partial differential equation is transformed to an ordinary one and solved. Finally, the modulation equation of viscoelastic piezoelectric nanoplates for combinational excitation is obtained. Emphasizing the effect of dual harmonic excitation and thermo-electro-mechanical loads on nonlinear frequency response of the system, jump and resonance phenomena are discussed. A detailed parametric study is conducted to examine the effect of nonlinearity, damping coefficient, nonlocal parameter, combinational excitation, electric voltage, initial stress and thermal environment.

Dynamic analysis of two collinear permeable Mode-I cracks in piezoelectric materials based on non-local piezoelectricity theory

Purpose Based on the non-local piezoelectricity theory, this paper is concerned with two collinear permeable Mode-I cracks in piezoelectric materials subjected to the harmonic stress wave. The paper aims to discuss this issue. Design/methodology/approach According to the Fourier transformation, the problem is formulated into two pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. Findings Finally, the dynamic non-local stress and the dynamic non-local electric displacement fields near the crack tips are obtained. Numerical results are provided to illustrate the effects of the distance between the two collinear cracks, the lattice parameter and the circular frequency of the incident waves on the entire dynamic fields near the crack tips, which play an important role in designing new structures in engineering. Originality/value Different from the classical solutions, the present solution exhibits no stress and electric displacement singularities at the crack tips in piezoelectric materials. It is found that the maximum stress and maximum electric displacement can be used as a fracture criterion.

Propagation of guided elastic waves in nanoscale layered periodic piezoelectric composites

Abstract This paper is concerned with the guided elastic waves propagating in nanoscale layered periodic piezoelectric composites. The equations of wave motion based on the nonlocal piezoelectricity continuum theory are derived, and the symmetric wave mode is considered. According to the continuity conditions of the mechanical and electric field quantities on the interface between the two neighboring sub-layers, we obtain the dispersion relation to analyze the behavior of the guided elastic waves and the influences of the nanoscale size-effect. A cut-off frequency appears when taking the nanoscale size-effect into consideration. The variations of the mechanical displacements and the electrical potential are calculated and discussed. The influences of the nanoscale size-effect and the volume fractions on the mode conversions are analyzed in details. It is found that all the dispersion curves including the mode conversion zones are compressed under the cut-off frequency. As the ratio of the internal to external characteristic lengths increases, the cut-off frequency decreases, while the frequency and the wave number of the mode conversion reduce. The present investigation may help us to control the cut-off frequency and the mode conversions by tuning the internal or external characteristic lengths and the volume fractions of the nanoscale layered periodic piezoelectric composites. The corresponding results may provide the theoretical basis for nanoscale wave device applications to control the wave mode conversions and the cut-off frequency.

Modified Continuum Mechanics Modeling on Size-Dependent Properties of Piezoelectric Nanomaterials: A Review.

Piezoelectric nanomaterials (PNs) are attractive for applications including sensing, actuating, energy harvesting, among others in nano-electro-mechanical-systems (NEMS) because of their excellent electromechanical coupling, mechanical and physical properties. However, the properties of PNs do not coincide with their bulk counterparts and depend on the particular size. A large amount of efforts have been devoted to studying the size-dependent properties of PNs by using experimental characterization, atomistic simulation and continuum mechanics modeling with the consideration of the scale features of the nanomaterials. This paper reviews the recent progresses and achievements in the research on the continuum mechanics modeling of the size-dependent mechanical and physical properties of PNs. We start from the fundamentals of the modified continuum mechanics models for PNs, including the theories of surface piezoelectricity, flexoelectricity and non-local piezoelectricity, with the introduction of the modified piezoelectric beam and plate models particularly for nanostructured piezoelectric materials with certain configurations. Then, we give a review on the investigation of the size-dependent properties of PNs by using the modified continuum mechanics models, such as the electromechanical coupling, bending, vibration, buckling, wave propagation and dynamic characteristics. Finally, analytical modeling and analysis of nanoscale actuators and energy harvesters based on piezoelectric nanostructures are presented.

Vibration analysis of piezoelectric ceramic circular nanoplates considering surface and nonlocal effects

Based on the theory of surface piezoelectricity and nonlocal piezoelectricity, a novel two-dimensional theory of piezoelectric nanoplates and boundary conditions are derived by utilizing the Hamilton’s principle. The free and forced vibrations of piezoelectric ceramic circular nanoplates are first investigated with the derived two-dimensional equations. Closed-form solutions are obtained and surface effects are examined. The results presented in this paper can be reduced to some classical ones theoretically and numerically. It has been revealed that the surface and nonlocal effects have a great influence on the performance of piezoelectric circular nanoplates in terms of resonant frequency, displacement, stress, electrical potential, current, capacitance ratio, and other quantities. A critical thickness of piezoelectric plate is calculated for the first time, below which the size-dependent effect is obvious that must be considered. These findings can provide effective guidance for the explanation of certain physical phenomenon about size-dependent electromechanical characteristics and experimental design of piezoelectric devices in nanoscale.

Anti-plane transverse waves propagation in nanoscale periodic layered piezoelectric structures

In this paper, anti-plane transverse wave propagation in nanoscale periodic layered piezoelectric structures is studied. The localization factor is introduced to characterize the wave propagation behavior. The transfer matrix method based on the nonlocal piezoelectricity continuum theory is used to calculate the localization factor. Additionally, the stiffness matrix method is applied to compute the wave transmission spectra. A cut-off frequency is found, beyond which the elastic waves cannot propagate through the periodic structure. The size effect or the influence of the ratio of the internal to external characteristic lengths on the cut-off frequency and the wave propagation behavior are investigated and discussed.

Fundamental formulations and recent achievements in piezoelectric nano-structures: a review

Piezoelectric nano-structures have been regarded as the next-generation piezoelectric material due to their inherent nano-sized piezoelectricity. This review summarizes the recent theoretical and experimental findings in piezoelectric nano-structures, including piezoelectric nanowires, nanoplates, nanobeams, nanofilms, nanoparticles, and piezoelectric heterogeneous materials containing piezoelectric nano-inhomogeneities. To begin, the types of piezoelectric nano-structured materials and the wide application of piezoelectric nano-structures in recent years are delineated. Next, the theoretical foundations including the definition of surface stress and electric displacement, the surface constitutive relations, the surface equilibrium equations, and nonlocal piezoelectricity, and their applications, are illustrated. Then, the effective mechanical and piezoelectric properties are depicted. Furthermore, the experimental investigations are classified, and some important observations are discussed. Finally, the perspectives and challenges for the future development of piezoelectric nano-structures are pointed out.

Mechanical Response of a Piezoelectrically Sandwiched Nano-beam Based on the Nonlocal Theory

A B S T R A C T This article deals with the mechanical analysis of a fixed-fixed nano-beam based on nonlocal theory of elasticity. The nano-beam is sandwiched with two piezoelectric layers through its upper and lower surfaces. The electromechanical coupled equations governing the problem are derived based on nonlocal theory of elasticity considering Euler-Berno ulli beam assumptions. Also, nonlocal piezoelectricity is according to Maxwell’s electrostatic equations. The piezoelectric layers are subjected to a voltage to tune the stiffness of the nano-beam. The equations are solved through step by step linearization method and Galerkin’s weighted residual method. The results are compared with those of the local model. The effect of piezoelectric voltages on the non-locality of the model is investigated as well .

Electrodynamics of memory-dependent nonlocal elastic continua

Balance laws and constitutive equations are given for elastic continua with memory of past motions and electromagnetic fields. Nonlinear, finite-linear, and linear constitutive equations are obtained and restricted by the second law of thermodynamics. Memory-dependent nonlocal piezoelectricity, piezomagnetism, heat and electric conduction, viscoelasticity, and other allied physical phenomena are in the domain of the general theory. The theory is applied to discuss infrared dispersion and lattice vibrations, natural optical activity, anomalous skin effect, and superconductivity, indicating the power and the potential of the nonlocal theory.