Piezoelectric Nanoplates Research Articles

Complete guided wave in piezoelectric nanoplates: A nonlocal stress expansion polynomial method

Taking the size-dependent and piezoelectric effect into account, the complete guided waves in nonlocal piezoelectric nanoplates are investigated. The Legendre polynomial method based on stress and electric displacement expansion is proposed to obtain the complete dispersion curves in the complex domain. The nonlocal and piezoelectric effects on propagative and evanescent waves are discussed. It is found that the nonlocal effect improves the phase velocity of complex Lamb wave, while reduces the attenuation and frequency bandwidth of complex Lamb wave. The stiffness-softening effect of the nonlocal structure reduces the phase velocity, cut-off frequency and escape frequency of propagative waves, while the stiffness-hardening effect of the piezoelectric structure increases the phase velocity, cut-off frequency and escape frequency of propagative waves. In addition, the nonlocal effect increases the piezoelectric effect, while the piezoelectric effect weakens the nonlocal effect on phase velocity.

Finite element modeling of mechanical behaviors of piezoelectric nanoplates with flexoelectric effects

Finite element modeling of mechanical behaviors of piezoelectric nanoplates with flexoelectric effects

Free vibration of circular and annular nanoplates with surface and flexoelectric effects

Free vibration of circular/annular piezoelectric nanoplates with flexoelectric and surface effects is studied. Using Hamilton’s principle, the governing equation and boundary conditions of circular/annular nanoplates are derived. Exact characteristic equations of clamped and simply-supported circular nanoplates are obtained. The static/dynamic flexoelectric and surface effects on the natural frequencies are analyzed. The results show that the flexoelectric and surface effects have obvious size effects. Positive surface stress increases the natural frequencies as if the nanoplate is tightened, and vice versa. There is a competitive mechanism between the influence of the flexoelectric and surface effects on the natural frequencies.

Electroelastic high-order computational continuum strategy for critical voltage and frequency of piezoelectric NEMS via modified multi-physical couple stress theory

piezoelectric structures can be used in many systems, such as nano-electromechanical systems (NEMS) and micro-electro-mechanical systems (MEMS) devices. This research aims to study a 2D-numerical nth-order solution strategy for investigating the stability and frequency characteristics of the nano-sized rectangular plate made of electrically materials. For modeling size-dependent factors of the piezoelectric NEMS, modified nonlocal couple stress theory (MNCST) with one length scale parameter and one nonlocal factor is presented. This theory adds symmetric rotation gradient tensor to the strain components. Also, the nonlocal theory is coupled with the time domains. First-order shear deformation plate theory (FSDT) is utilized for modeling the electrically nanoplate structure. Hamilton’s principle is used for obtaining the governing equations of the current nanostructure. Consequently, an attempt is carried out to investigate the impacts of the geometry of nanoplate, applied voltage, length scale, and nonlocal parameters on the frequency performance of the three-dimensional nano-sized electrically plate. The results show that, When the foundation is considered, the effect of the length of the nanoplate on the critical voltage of a piezoelectric nanoplate reduces. As another important outcome, there is a direct relation between l/h factor and dynamic stability of the piezoelectric nanoplate, but at the greater value of l/h factor, there is not any change in the frequency of the nanosystem due to increasing this factor.

Reflection and transmission of elastic waves through nonlocal piezoelectric plates sandwiched in two solid half-spaces

A nonlocal stress expansion Legendre orthogonal polynomial method is proposed to study the reflection and transmission of elastic waves through piezoelectric nanoplates sandwiched in two solid half-spaces. The proposed method avoids employing the relationship between local stress and nonlocal stress to construct boundary conditions. The reflection and transmission of plane waves and out-plane waves are studied separately with considering the electrical open circuit boundary. The convergence of presented method is discussed. The correctness of presented method is verified by comparing with the published data of piezoelectric nanoplates immersed in water, which can be considered as a simplified situation sandwiched in two solid half spaces. In addition, the nonlocal effect on the wave mode conversion, stress and electric displacement distribution, and piezoelectricity are discussed. Results show that the nonlocal effect reconstructs the wave mode conversion, and enhances the influence of the piezoelectricity on the critical angle.

Analysis of Flexural Vibrations of a Piezoelectric Semiconductor Nanoplate Driven by a Time-Harmonic Force.

The performance of devices fabricated from piezoelectric semiconductors, such as sensors and actuators in microelectromechanical systems, is superior; furthermore, plate structures are the core components of these smart devices. It is thus important to analyze the electromechanical coupling properties of piezoelectric semiconductor nanoplates. We established a nanoplate model for the piezoelectric semiconductor plate structure by extending the first-order shear deformation theory. The flexural vibrations of nanoplates subjected to a transversely time-harmonic force were investigated. The vibrational modes and natural frequencies were obtained by using the matrix eigenvalue solver in COMSOL Multiphysics 5.3a, and the convergence analysis was carried out to guarantee accurate results. In numerical cases, the tuning effect of the initial electron concentration on mechanics and electric properties is deeply discussed. The numerical results show that the initial electron concentration greatly affects the natural frequency and electromechanical fields of piezoelectric semiconductors, and a high initial electron concentration can reduce the electromechanical fields and the stiffness of piezoelectric semiconductors due to the electron screening effect. We analyzed the flexural vibration of typical piezoelectric semiconductor plate structures, which provide theoretical guidance for the development of new piezotronic devices.

Wave Propagation in Graphene Platelet-Reinforced Piezoelectric Sandwich Composite Nanoplates with Nonlocal Strain Gradient Effects

Wave Propagation in Graphene Platelet-Reinforced Piezoelectric Sandwich Composite Nanoplates with Nonlocal Strain Gradient Effects

Novel Nanoelectromechanical System Pressure Biosensing Method for Early Detection of Cholesterol Accumulation in Blood Vessels

High cholesterol could be dangerous, along with the deposits of other substances, such as fat, on the walls of the arteries. These plaques can reduce blood flow through the arteries, which in turn can cause complications such as chest pain, blood clots, and heart attack. Hence, there is a need for an efficient way to measure the concentration of cholesterol in blood vessels with great accuracy to predict its risk on health. The present study aims to measure the concentration of cholesterol and track it accurately in the blood vessels using an ultrasound pressure sensor, which detects the concentration of cholesterol and produces a pressure field around its surface that is directly proportional to the concentration. This field can be tracked by ultrasound. In this study, the experiments conducted involved the insertion of aluminum nanoparticles, which represent a pressure sensor coated with a massless piezoelectric aluminum nitride nanoplate, into simulated blood vessels containing different concentrations that mimic human blood. The sensitivity of the blood vessels was monitored at different time periods. Moreover, an experimental setup was constructed to validate the possibility of using existing ultrasound medical imaging technologies in tracking the proposed nano biosensors. The setup involves prototyping a medical phantom with a specific acoustic characteristic for simulating human tissues. Various clinical scenarios have been imitated and the possibility of tracking these novel micro electromechanical pressure biosensors has been discussed.

A comprehensive nonlocal surface-piezoelectricity model for thermal and vibration analyses of piezoelectric nanoplates

The present study employs the modified shear deformation plate theories to investigate the effects of surface parameters on the electro-thermal vibration characteristics of the piezoelectric nanoplates. The nonlocal surface piezoelectricity theory based on Gurtin-Murdoch surface elasticity and Eringen’s nonlocal theory are incorporated to take the small-scale effects into account. The governing equations of motion of the structure are derived and solved using the Hamilton’s principle and Galerkin method. Validity of the proposed model is demonstrated by comparing the results with those available in the literature. The verified model is employed to investigate the effects of different parameters such as surface residual stress, surface elastic constants, surface piezoelectricity, nonlocal parameter, aspect ratio, thickness ratio, temperature, and applied voltage on the dynamic characteristics of the structure. The results report significant contribution of the surface parameters in vibration characteristics of the piezoelectric nanoplates.

Thermo-electro-mechanical vibration and buckling analysis of quadrilateral and triangular nanoplates with the nonlocal finite strip method

As a first endeavor, thermo-electro-mechanical analysis of quadrilateral and triangular piezoelectric nanoplates are investigated based on the nonlocal theory and the Kirchhoff plate theory. It is assumed that the piezoelectric nanoplate is subjected to a biaxial force, an external electric voltage, and a uniform temperature rise. Hamilton’s principle is employed to derive the governing equations. The B3-spline finite strip method used to determine the natural frequencies, buckling loads, and corresponding mode shapes of displacement and the electric potential of quadrilateral and triangular piezoelectric nanoplates, for the first time. The comprehensive parametric study is conducted to explore the effect of the nonlocal parameter, geometrical shape, thermo-electro-mechanical loadings, boundary conditions, aspect ratio, and side length. It is shown that small-scale effect plays a considerable role in the buckling and vibration behavior of quadrilateral and triangular piezoelectric nanoplates.

Flexoelectric effects on the natural frequencies for free vibration of piezoelectric nanoplates

Flexoelectricity is an electromechanical coupling phenomenon between polarization and strain gradient. Based on the Kirchhoff thin plate theory, the electromechanical coupling responses of nanoplates with the piezoelectric and flexoelectric effects are studied in this paper. Free vibration of a piezoelectric nanoplate with consideration of flexoelectricity is analyzed with emphasis on the influence of the dynamic flexoelectric effect on the natural frequencies. By means of Hamilton’s variational principle, the governing equation of rectangular plates together with associated boundary conditions is derived. The natural frequencies are evaluated for a nanoplate simply supported at two opposite edges, and exact frequency equations are obtained for the other two opposite edges being simply supported, clamped–clamped, clamped–free, simply supported–free, or clamped–simply supported. The influence of dynamic flexoelectricity on the natural frequencies is elucidated. The results show that the dynamic flexoelectric effect is also size-dependent; the smaller the plate thickness is, the more obvious the dynamic flexoelectric effect is. The results also show that the dynamic flexoelectric effect is more pronounced when the order of vibration modes is higher and nanoplate’s side ratio is larger. The positive and negative choice of static and dynamic flexoelectric coefficients have completely different effects on the natural frequencies. The influence of the dynamic flexoelectric effect on the natural frequencies is closely related to the side constraint and geometry of the plate. The piezoelectric effect does not alter the natural frequencies for free vibration of a homogeneous nanoplate.

Studies on calculation method and bandgap properties of a nonlocal piezoelectric phononic crystal nanoplate

By introducing nonlocal elastic theory and Kirchhoff plate theory to plane wave expansion (PWE) method, the band structure of a nonlocal piezoelectric phononic crystal (PC) nanoplate is calculated. A complete band gap with magnitude order gigahertz (GHz) is opened. In order to investigate the characteristics of such a band gap in detail, the corresponding influence rules of thermo-electro-mechanical coupling fields, nonlocal effects and geometric parameters on band gaps are studied. During the researches, temperature variation, electrical voltage and external axial force are picked as the influencing parameters corresponding to thermo-electro-mechanical coupling fields. Nonlocal coefficient is chosen as the influencing parameter related to surface effects. Lattice constant, PZT-4 hole radius and nanoplate thickness are picked as the influencing parameters of geometric parameters. All the results are expected to be of help for nano electro mechanical system (NEMS) based on piezoelectric periodic nanoplates.

Buckling and Vibration Analysis of a Double-layer Graphene Sheet Coupled with a Piezoelectric Nanoplate

In this article, the vibration and buckling of a double-layer Graphene sheet (DLGS) coupled with a piezoelectric nanoplate through an elastic medium (Pasternak and Winkler models) are under consideration. DLGS are subjected to biaxial in-plane forces and van der Waals force existing between each layer. Polyvinylidene fluoride (PVDF) piezoelectric nanoplate is subjected to an external electric potential. For the sake of this study, sinusoidal shear deformation theory of orthotropic plate expanded with Eringen’s nonlocal theory is selected The results indicate that nondimensional frequency and nondimensional critical buckling load rise, when the ratio of width to thickness increases. Furthermore, incrementing the effect of elastic medium parameter results in increasing the stiffness of the system and, consequently, rising nondimensional frequency and critical buckling load.

Nonlinear dynamics and vibration of reinforced piezoelectric scale-dependent plates as a class of nonlinear Mathieu–Hill systems: parametric excitation analysis

This work is motivated by little research in the nonlinear dynamic instability of the reinforced piezoelectric nanoplates. This paper, using an analytical approach, presents bifurcations in the nonlinear dynamic instability of the reinforced piezoelectric nanoplates caused by the parametric excitation. An axial parametric load is applied to excite the system, while the reinforced piezoelectric nanoplate is under an applied electric voltage, simultaneously. The governing equations of motion for the reinforced piezoelectric nanoplate embedded on a visco-Pasternak foundation are derived using the nonlocal elasticity theory, Hamilton’s principle, and nonlinear von Karman theory. A class of nonlinear the Mathieu–Hill equation is established to determine the bifurcations and the regions of the nonlinear dynamic instability. The numerical results are performed, while the emphasis is placed on investigating the effect of the applied electric voltage, visco-Pasternak foundation coefficients, and the parametric excitation. It is found that the damping coefficient is responsible of the bifurcation point variation, while the amplitude response depends on the term of the natural frequency.

Effect of residual surface stress on parametrically excited nonlinear dynamics and instability of viscoelastic piezoelectric nanoelectromechanical resonators

The present study mainly investigates the effect of the residual surface stress and the applied electric voltage on the nonlinear dynamic instability of the viscoelastic piezoelectric nanoresonators under parametric excitation. In fact, great attention is given to the influence of the residual surface stress on the nonlinear instability of the system. Numerical examples are treated which show various bifurcations. By means of a bifurcation analysis, it is shown that the instability of the system can be significantly affected by considering the residual surface effect. The results also show that a discontinuous bifurcation is always accompanied by a jump. Finally, stable and unstable regions in dynamic instability of viscoelastic piezoelectric nanoplates are addressed.

High figure-of-merit NEMS thermal detectors based on 50-nm thick AlN nano-plate resonators

This paper reports on the demonstration of ultrafast (thermal time constant, τ ∼ 166 μs) and high resolution (noise equivalent power, NEP ∼ 549 pW/Hz1/2) thermal detectors based on high quality factor 50-nm thick aluminum nitride (AlN) piezoelectric resonant nanoplates. Here we show that by employing nanoscale (30 nm) aluminum anchors, both high thermal resistance (Rth ∼ 1.1 × 106 K/W) and high quality factor (Q ∼ 1000) can be achieved in greatly scaled AlN nanoplate resonators. Furthermore, the absorptance of such ultrathin AlN resonators was characterized, in mid-wavelength infrared region showing an average absorptance of ∼36% from 2.75 μm to 6.25 μm. These unique features were exploited for the experimental demonstration of AlN NEMS resonant thermal detectors with greatly reduced thermal capacitance and over doubled figure of merit [FoM = 1/(NEP × τ)] compared to what was previously achieved by the same technology.

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.

Studies on thermo-electro-mechanical coupling bandgaps of a piezoelectric phononic crystal nanoplate with surface effects

Applying surface piezoelectricity theory and plane wave expansion (PWE) method to the model of Kirchhoff plate, the calculation method of band structure of a piezoelectric phononic crystal (PC) nanoplate with surface effects is proposed and formalized. In order to investigate the bandgap properties of first order in the nanoplate in detail, the corresponding influence rules of thermo-electro-mechanical coupling fields, surface effects and geometric parameters on bandgaps are studied. During the researches, temperature variation, electrical voltage and external axial force are picked as the influencing parameters corresponding to thermo-electro-mechanical coupling fields. Residual surface stress and material intrinsic length are chosen as the influencing parameter related to surface effects. Lattice constant, radius of PZT-4 hole and thickness of nanoplate are picked as the influencing parameters of geometric parameters. All the results are expected to be helpful for the design of micro and nanodevices based on piezoelectric periodic nanoplates.

An analytical study of vibration in functionally graded piezoelectric nanoplates: nonlocal strain gradient theory

In this paper, we analytically study vibration of functionally graded piezoelectric (FGP) nanoplates based on the nonlocal strain gradient theory. The top and bottom surfaces of the nanoplate are made of PZT-5H and PZT-4, respectively. We employ Hamilton’s principle and derive the governing differential equations. Then, we use Navier’s solution to obtain the natural frequencies of the FGP nanoplate. In the first step, we compare our results with the obtained results for the piezoelectric nanoplates in the previous studies. In the second step, we neglect the piezoelectric effect and compare our results with those obtained for the functionally graded (FG) nanoplates. Finally, the effects of the FG power index, the nonlocal parameter, the aspect ratio, and the side-tothickness ratio, and the nanoplate shape on natural frequencies are investigated.

Parametrically excited nonlinear dynamic instability of reinforced piezoelectric nanoplates

The nonlinear dynamic instability of reinforced piezoelectric nanoplates exposed to a parametric excitation and an electric voltage is the objective of the present paper. Firstly, a piezoelectric nanoplate reinforced with two graphene layers and resting on a visco-elastic foundation is modeled. Secondly, the piezoelectric nonlocal elasticity theory, the Kelvin-Voigt model, von Karman nonlinear relations and Hamilton’s principle, respectively, are used to derive the nonlinear governing differential equation of motion. In the next step, to transform partial differential equation to ordinary one and then, solve the equation, the Galerkin technique and multiple time scales method are employed respectively. At the end, the modulation equation of reinforced piezoelectric nanoplates is obtained. Emphasizing the effect of the electric voltage and parametric excitation on dynamic instability of the system, trivial and nontrivial steady-state solutions are discussed. The main results emphasize that the damping coefficient is responsible of the bifurcation point variation, while the amplitude response depends on the term of natural frequency. Therefore, damping can have a strong influence on the system.