Piezoelectric Body Research Articles

Shear horizontal surface waves in piezoelectric materials with surface stress

ABSTRACTThe propagation of shear horizontal (SH) surface waves in piezoelectric semi-infinite bodies is investigated theoretically. The surface stress exerting on the boundary is taken into account through surface piezoelectricity theory, and the velocity ranges and existence conditions of such surface waves for both electrically open and shorted cases are derived in detail. Analysis results show that the SH surface waves occurring with surface stress are dispersive in contrast to the classical situation, and the propagation characteristics strongly depend on the relative value of surface elasticity, surface piezoelectricity and surface density.

Vibrations of inhomogeneous piezoelectric bodies in conditions of residual stress–strain state

• The linearized statement for inhomogeneous piezoelectric prestressed body is derived. • The general variational principles and weak formulations of the original problem are described. • Particular boundary problems for rods and thin disk are investigated. • A formula for frequency change as a function of residual stress level is obtained. • An effect of residual stress on frequency response functions for a disk is estimated. In the article, we present the general linearized statement of the boundary problem on vibrations of inhomogeneous piezoelectric body under residual stress–strain state. We have derived the weak statement of the problem for the test functions satisfying the essential boundary conditions, formulated the general variational principle for a prestressed piezoelectric body and proposed several options for the potential energy representation. On the basis of the principles proposed, we have formulated and investigated a number of particular boundary problems on steady-state vibrations of inhomogeneous piezoelectric prestressed rods and thin prestressed disk polarized in the direction of thickness. The analysis of the residual stress levels on frequency response function for the bodies considered is provided.

Analysis of a Dynamic Contact Problem for Electro-viscoelastic Materials

We consider a mathematical model which describes the dynamic process of contact between a piezoelectric body and an electrically conductive foundation. We model the material’s behavior with a nonlinear electro-viscoelastic constitutive law; the contact is frictionless and is described with the normal compliance condition. We derive variational formulation for the model which is in the form of a system involving the displacement field, the electric potential field, the damage field and the adhesion field. We prove the existence of a unique weak solution to the problem. The proof is based on arguments of time dependent variational inequalities, parabolic inequalities, differential equations and fixed point.

Variational and Numerical Analysis of a Static Thermo-Electro-Elastic Problem with Friction

We consider a mathematical model which describes a static frictional contact between a piezoelectric body and a thermally conductive obstacle. The constitutive law is supposed to be thermo-electro-elastic and the contact is modeled with normal compliance and a version of Coulomb’s friction law. We derive a variational formulation of the problem and we prove the existence and uniqueness of its solution. The proof is based on some results of elliptic variational inequalities and fixed point arguments. Furthermore, a finite element approximation and a priori error estimates are obtained.

An initial boundary value problem for modeling a piezoelectric dipolar body

This study deals with the first initial boundary value problem in elasticity of piezoelectric dipolar bodies. We consider the most general case of an anisotropic and inhomogeneous elastic body having a dipolar structure. For two different types of restrictions imposed on the problem data, we prove two results regarding the uniqueness of solution, by using a different but accessible method. Then, the mixed problem is transformed in a temporally evolutionary equation on a Hilbert space, conveniently constructed based on the problem data. With the help of a known result from the theory of semigroups of operators, the existence and uniqueness of the weak solution for this equation are proved.

A biomimetic vibration sensor using a symmetric electrodes metal core piezoelectric fiber

A biomimetic vibration sensor to sense external vibrations was designed based on the hair receptor of insects similar to the water strider. Platinum core piezoelectric ceramic fiber body was prepared by squeeze and press method. This was followed by high-temperature sintering, surface electrode coating, and polarizing to fabricate the symmetric coated metal core piezoelectric fiber vibration sensor. A cantilever beam structure with two surface electrodes was designed as the theoretical sensor model. The fiber was fixed on a matrix structure. Experiments were performed to verify sensing characteristics under impact vibration and simple harmonic excitation. Results showed that the symmetric coated metal core piezoelectric fiber was able to sense amplitude and direction of impact vibration along with frequency, amplitude, and direction under simple harmonic excitation. Such a biomimetic vibration sensor can be effectively used to sense vibration amplitude and direction for a wide range of applications.

Analytical technique for thermoelectroelastic field in piezoelectric bodies with D∞ symmetry in cylindrical coordinates

ABSTRACTA general solution technique for non-axisymmetric thermoelectroelastic problems in cylindrical domains with D∞ symmetry is constructed. The displacement and electric field are expressed in terms of the respective potential functions, and the thermoelectroelastic field quantities are expressed in terms of the elastic and piezoelastic potential functions, each of which essentially satisfies a Laplace equation with respect to the spatial coordinates, combined with the two thermoelastic displacement potential functions. As an application of the technique, the theoretical analysis of a solid cylinder subjected to combined mechanical and thermal loading is performed, and the necessity of the thermoelectroelastic analyses is demonstrated.

Electro-elastic fields in an elliptic piezoelectric plane with an elliptic hole or a crack of arbitrary location

Electro-elastic fields in an elliptic piezoelectric plane with an elliptic hole or a crack of arbitrary location are studied based on the complex variable method and the assumption that the elliptic hole or the crack is impermeable to an electric field. The novel feature of the present work is to construct the complex potentials in a finite piezoelectric body with Faber series containing unknown coefficients. Using the given boundary conditions, the coefficients can be solved, and then the electro-elastic fields in the plane can be calculated. Finally, numerical examples are given for the electro-elastic fields in the plane and the electro-elastic intensity factors at the crack tips when the hole degenerates into a crack. It is found that the sizes of the elliptic plane and the elliptic hole (or the crack) have a great influence on electro-elastic fields (or the intensity factors of the crack).

The energy method for solving electroacoustic problems using combining finite element analysis and analytical methods

The energy method for solving electroacoustic transducer problems requires calculation of the electrical, mechanical and electromechanical energies of a piezoelectric body from the vibration mode shapes, which are often difficult to obtain analytical particularly with structures having complex boundary conditions. An alternative approach is to determine the vibration mode shapes either experimentally or by finite element analysis and to proceed with computing the energies analytically. The frequency response can then be determined from an equivalent electromechanical circuit approach. An example of this hybrid approach applied to a flextensional transducer will be presented with comparison to experimental results. [Work supported by ONR Code 321.]

Frequency dependence of electromagnetic radiation from a finite vibrating piezoelectric body

We study electromagnetic radiation from a finite piezoelectric body in time-harmonic vibration through the analysis of piezoelectric crystal plate resonators. The polarization charge and free charge involved are obtained. To the lowest order, the charges are approximated by a vibrating electric dipole whose radiated power is then calculated. It is shown that the radiated power is formally proportional to the fourth power of the vibration frequency. As a consequence, the radiated power increases rapidly when the body becomes smaller, which is relevant in the miniaturization of resonant piezoelectric devices.

Analysis of a dynamic viscoelastic-viscoplastic piezoelectric contact problem

In this paper, we study, from both variational and numerical points of view, a dynamic contact problem between a viscoelastic-viscoplastic piezoelectric body and a deformable obstacle. The contact is modelled using the classical normal compliance contact condition. The variational formulation is written as a nonlinear ordinary differential equation for the stress field, a nonlinear hyperbolic variational equation for the displacement field and a linear variational equation for the electric potential field. An existence and uniqueness result is proved using Gronwall's lemma, adequate auxiliary problems and fixed-point arguments. Then, fully discrete approximations are introduced using an Euler scheme and the finite element method, for which some a priori error estimates are derived, leading to the linear convergence of the algorithm under suitable additional regularity conditions. Finally, some two-dimensional numerical simulations are presented to show the accuracy of the algorithm and the behaviour of the solution.

Theoretical Analysis of Thermoelectroelastic Field in D∞-Piezoelectric Bodies

Theoretical Analysis of Thermoelectroelastic Field in D∞-Piezoelectric Bodies

Analytical technique for thermoelectroelastic field in piezoelectric bodies with D∞ symmetry

ABSTRACTA general solution technique for thermoelectroelastic problems in bodies with D∞ symmetry is constructed. The displacement and electric field are expressed in terms of the respective potential functions, and the thermoelectroelastic field quantities are expressed in terms of the elastic and piezoelastic potential functions, each of which satisfies the Laplace equation with respect to the appropriately transformed spatial coordinates, combined with the two thermoelastic displacement potential functions. As an application of the technique, the theoretical analysis of a semi-infinite body subjected to a temperature distribution is performed, and the significance of the thermoelectroelastic analyses is demonstrated.

Asymptotic curved interface models in piezoelectric composites

We study the electromechanical behavior of a thin interphase, constituted by a piezoelectric anisotropic shell-like thin layer, embedded between two generic three-dimensional piezoelectric bodies by means of the asymptotic analysis in a general curvilinear framework. After defining a small real dimensionless parameter ε, which will tend to zero, we characterize two different limit models and their associated limit problems, the so-called weak and strong piezoelectric curved interface models, respectively. Moreover, we identify the non-classical electromechanical transmission conditions at the interface between the two three-dimensional bodies.

A general solution technique for electroelastic fields in piezoelectric bodies with D ∞ symmetry in cylindrical coordinates

To elucidate the electroelastic field in bodies with D ∞ symmetry such as wooden materials, we constructed a general solution technique for electroelastic problems in such bodies in a cylindrical coordinate system. We introduced the displacement and electric potential functions to express the displacement and electric field in cylindrical coordinates; their governing equations were obtained using the fundamental equations for the electroelastic field. The electroelastic field quantities could be expressed in terms of two elastic displacement potential functions and two piezoelastic displacement potential functions, each of which satisfies a Laplace equation with respect to the appropriately transformed cylindrical coordinates. As an application of the technique, we analyzed the problem of an infinitely long cylinder subjected to a non-axisymmetrically distributed electric surface potential. Using numerical calculations, we elucidated the electroelastic field quantities within the cylinder and found unique electroelastic coupling behaviors, which clearly demonstrate the necessity for the analytical technique presented. Moreover, we confirmed the possibility of the nondestructive evaluation (NDE) techniques by use of the piezoelectric effects.

VARIATIONAL ANALYSIS OF AN ELECTRO-VISCOELASTIC CONTACT PROBLEM WITH FRICTION AND ADHESION

We consider a mathematical model which describes the qua- sistatic frictional contact between a piezoelectric body and an electri- cally conductive obstacle, the so-called foundation. A nonlinear electro- viscoelastic constitutive law is used to model the piezoelectric mate- rial. Contact is described with Signorini's conditions and a version of Coulomb's law of dry friction in which the adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation. We derive a variational formula- tion for the model, in the form of a system for the displacements, the electric potential and the adhesion. Under a smallness assumption which involves only the electrical data of the problem, we prove the existence of a unique weak solution of the model. The proof is based on arguments of time-dependent quasi-variational inequalities, differential equations and Banach's fixed point theorem.

A micro-machined hydrophone employing a piezoelectric body combined on the gate of a field-effect transistor

We report a micro-machined hydrophone using piezoelectric gate on a field-effect transistor (PiGoFET), where a piezoelectric body is combined directly on the gate of a FET. The PiGoFET transduction mechanism decouples the sensitivity from the dimensions of the piezoelectric body, enabling the miniaturization of hydrophones. Here we exploit the PiGoFET mechanism for hydrophone miniaturization, which is realized via hybrid bonding integration to fabricate a micro-PiGoFET in a CMOS-compatible manner. The hybrid bonding integration employs separate wafers for the piezoelectric MEMS and CMOS processes, which are combined via eutectic wafer bonding to complete the micro-PiGoFET device. A micro-PiGoFET hydrophone was designed, fabricated and characterized with a measured sensitivity of −191.5dB±1dB (Ref.V/μPa) for frequencies in the range 50–1000Hz. These results demonstrate the potential for high-performance miniaturized hydrophone systems for wide-band and low-frequency applications, as well as system-on-chip functionality.

A Quasistatic Electro-Viscoelastic Contact Problem with Adhesion

The aim of this paper is to study the process of contact with adhesion between a piezoelectric body and an obstacle, the so-called foundation. The material’s behavior is assumed to be electro-viscoelastic; the process is quasistatic, the contact is modeled by the Signorini condition. The adhesion process is modeled by a bonding field on the contact surface. We derive a variational formulation for the problem and then we prove the existence of a unique weak solution to the model. The proof is based on a general result on evolution equations with maximal monotone operators and fixed-point arguments.

Natural vibrations of nanodimensional piezoelectric bodies with contact-type boundary conditions

Homogeneous problems of vibrations of nanodimensional piezoelectric bodies with surface stresses and electric charges taken into account are studied. The boundary conditions modeling the frictionless contact of a body with rigid massive punches and the body coverings by a system of open and grounded electrodes are considered. The weak statements of these problems are given. It is proved that the spectrum is real and discrete and the system of eigenfunctions is complete. Several theorems on the eigenfrequency variations are stated with the surface effects taken into account and in the case of variations in the mechanical and electrical boundary conditions and the material characteristics. The finite element approximations are used to state finite-dimensional generalized eigenvalue problems. The results of finite-element calculations of the model problem, which illustrate the influence of surface effects, are given.

A new transduction mechanism for hydrophones employing piezoelectricity and a field-effect transistor

In contrast to the induced charge or voltage in conventional piezoelectric hydrophones, changes in the bound surface charge density and the corresponding changes in the electric field from a piezoelectric body do not depend on the size of the piezoelectric material. In this paper, we describe a new transduction mechanism, the piezoelectric gate on a field-effect transistor (PiGoFET), for applications in hydrophones. We describe a theoretical model of the PiGoFET, which shows that high sensitivity can be achieved with a small hydrophone due to the size independence of the PiGoFET transduction mechanism. A PiGoFET hydrophone was designed, fabricated, and characterized. The measured sensitivity was −175.5±1dB (Ref. V/μPa) at frequencies in the range 50–500Hz. The measured frequency response was in agreement with the simulated data to within 2dB. These results demonstrate potential applications in hydrophones, especially for wide-band and low-frequency applications, as well as in micro-hydrophones.