Boundary-value Problem Of Electroelasticity Research Articles

РЕЗОНАНСНЫЕ ХАРАКТЕРИСТИКИ СОРБЦИОННОГО ОПТОВОЛОКОННОГО ПЬЕЗОЭЛЕКТРОЛЮМИНЕСЦЕНТНОГО ДАТЧИКА

A mathematical electro-mechanical model of a representative fragment of a gas-analytical optical fiber piezoelectroluminescent sensor with a special external absorption layer for monitoring extended areas has been developed. Informative light signal is generated as a result of mechanoluminescent effect caused by contact interaction of piezoelectric and electroluminescent cylindrical layers (coatings) of fiber in case of forced electromechanical vibrations of sensor under action of applied harmonic control electric voltage. The algorithm for finding the sorption spectrum (changes in the density of the absorption layer along the length of the sensor) is presented through the solution of the Fredholm integral equation based on the results of measuring the informative light spectrum of the intensity of the light at the output from the fiber of the sensor. Numerical solution of coupled stationary boundary value problem of electroelasticity for representative fragment of sensor is implemented. Natural frequencies and shapes of sensor oscillations were found taking into account geometric shape, relative location and anisotropy of electroelastic properties of its structural elements, including characteristics of absorption layer. Regularities of influence of diagnosed value of absorption layer density on informative values of resonance frequencies of different forms of sensor oscillations were revealed.

Numerical analysis of the effective properties of inhomogeneously polarized porous piezoelectric ceramics with ni-doped pore walls taking into account the influence of volume fractions of metal and pores

The paper considers a porous piezoelectric composite with metal layers deposited on the interface between the piezoelectric and vacuum phases. Such metal layers can be added technologically to improve the mechanical and electromechanical properties of the composite. To find the effective moduli, we designed a simple representative cubic volume of a unit cell consisting of a piezoelectric matrix with a compound spherical pore in its center. In turn, the compound pore includes the pore itself and a hollow metal sphere on its surface. The composite's three phases were all modeled as piezoelectric materials. The conducting interface layer was modeled as a piezoelectric material with very high dielectric constants, small piezoelectric moduli, and elastic properties of the employed metal, while the vacuum pore was modeled as a piezoelectric material with marginal moduli. The mathematical formulation of boundary value homogenization problems with full contact conditions on the interface boundaries, based on the Hill energy criterion, was described. By solving nine boundary value problems of electroelasticity with different boundary conditions for displacements and electric potential by the finite element method, a complete set of effective moduli of the piezoelectric composite is determined. The importance of considering the inhomogeneous polarization due to the presence of pores and metallic inclusions was discussed. An approximate method was proposed for determining the inhomogeneous polarization field in a piezoceramic matrix, based on a preliminary solution of the electrostatic problem for dielectrics and locating the element coordinate systems rotated along the polarization vector. The paper describes the results of computational experiments for a piezocomposite consisting of PZT-5H piezoceramic matrix, pores, and nickel layers on the pore surfaces. Comparisons between the effective properties of this composite with different volume fractions of metal and the conventional porous piezocomposite were provided, depending on the porosity and taking into account the inhomogeneous polarization. Significant differences were observed for some piezomoduli and dielectric constants, which are promising for various practical applications of the considered composites in piezoactuators using the phenomenon of the transverse piezoelectric effect.

Development of a structurally similar element of a helicopter blade with an active twist system

A mathematical model is formulated for calculating the stress-strain state (SSS) of piezoelectric layered polymer composite materials (PCM) equipped with a control piezoactuator. The model implements the principle of thermo-piezoelectric analogy, which allows to move from the coupled boundary value problem of electroelasticity to the boundary value problem of thermoelasticity. The mathematical model was tested with a numerical calculation of the mechanical behavior of a sample structurally similar to a rotor blade, equipped with control piezo-actuators and made of equal strength and unidirectional fiberglass.

Asymptotic Solutions of Boundary Value Problems of Electroelasticity for Transversely Isotropic Toroidal Shells Made of Piezoceramic Materials

By asymptotic integration of the equations and relations of a three-dimensional problem of electroelasticity theory for transversely isotropic ceramics, boundary-value problems for a thin toroidal shell are solved in the cases where the conditions of the first, second, or mixed dynamic boundary-value problems of elasticity theory are given on its surface. Recurrent formulas for calculating components of the displacement vector and stress tensor and the electric field potential in thickness-polarized ceramics are deduced. The resonance frequencies are also found.

Boundary value problems of electroelasticity for a plate with an inclusion and a half-space with a slit

Problems of determining the mechanical and electrical fields in a piezoelectric plate reinforced with an inclusion or in a half-space weakened by a cut are considered. Using the methods of the theory of analytic functions these problems are reduced to a system of singular integro-differential equations (for a plate) or to a singular integral equation with a fixed singularity (for a half-space). Approximate and exact solutions of the problems are obtained by the method of orthogonal polynomials and integral transforms.

Piezocomposite with reciprocal polarization of oriented ellipsoidal inclusions and the matrix

We consider statistically homogeneous two-phase random piezoactive structures with deterministic properties of inclusions and the matrix and with random mutual location of inclusions. We present the solution of a coupled stochastic boundary value problem of electroelasticity for the representative domain of a matrix piezocomposite with a random structure in the generalized singular approximation of the method of periodic components; the singular approximation is based on taking into account only the singular component of the second derivative of the Green function for the comparison media. We obtain an analytic solution for the tensor of effective properties of the piezocomposite in terms of the solution for the tensors of effective properties of a composite with an ideal periodic structure or with the “statistical mixture” structure and with the periodicity coefficient calculated for a given random structure with its specific characteristics taken into account. The effective properties of composites with auxiliary structures (periodic and “statistical mixture”) are also determined in the generalized singular approximation by varying the properties of the comparisonmedium. We perform numerical computations and analyze the effective properties of a quasiperiodic piezocomposite with reciprocal polarization of oriented ellipsoidal inclusions and the matrix, the layered structures with reciprocal polarization of the layers [1] of a polymer piezoelectric PVF, and find their unique properties such as a significant increase in the Young modulus along the normal to the layers and in dielectric permittivities, the appearance of negative values of the Poisson ratio under extension along the normal, and an increase in the absolute values of the basic piezomoduli.

Solution of initial–boundary-value problems of electroelasticity revisited

The Hamilton-Ostrogradsky principle is used to substantiate the statement of initial-boundary-value problems of electroelasticity. The free vibrations of a piezoceramic layer are used as an example to illustrate some features of solving nonstationary problems of electroelasticity

Boundary-value problem of electroelasticity for a piezoceramic elliptic cylinder and a layer with tunnel hollow

We consider a skew-symmetric stressed state of a piezoceramic layer weakened by a through elliptic hollow filled with air. The surfaces of the layer (or a finite elliptic piezoceramic cylinder) operating in contact with air are covered with a diaphragm rigid in its plane and flexible in the perpendicular direction. The stress vector {X1, X2, X3} acts on the lateral surface. The boundary-value problem of electroelasticity is reduced to a system of singular integral equations. This system is numerically solved by the method of mechanical quadratures. The integral representations of the solutions are constructed on the basis of the corresponding matrix of Φ-solutions. The distribution of normal circular stresses over the elliptic contour subjected to the action of normal or tangential stresses is investigated.

Averaging of the physicomechanical characteristics of piezocomposites (plane deformation)

The mechanical, electric, and piezoelectric characteristics of fibrous piezocomposites with doubly periodic system of fibers are averaged within the framework of a model of regular structures under the conditions of plane deformation. It is shown that, for the general case of stacking of fibers with arbitrary cross section, the problem is reduced to the determination of certain functionals specified by a system of linear algebraic and singular integral equations of the corresponding boundary-value problem of electroelasticity for the analyzed structure.

Application of Singular Integral Equations in the Boundary Value Problems of Electroelasticity

Abstract The purpose of this paper is to consider the three-dimensional versions of the theory of electroelasticity for a transversally esotropic body. Applying the potential method and the theory of singular integral equations, the normality of singular integral equations corresponding to the boundary value problems of electroelasticity are proved and the symbolic matrix is calculated. The uniqueness and existence theorem for the basic BVPs of electroelasticity are given.

Investigation of the direct and inverse piezoeffect in the dynamic problem of electroelasticity for an unbounded medium with a tunnel opening

An effective approach to the investigation of antiplane electroacoustic wave fields in an unbounded piezoelectric medium weakened by a tunnel opening with the given system of surface electrodes is suggested. The approach is based on the method of boundary integral equations. It is assumed that the medium excitation occurs due to the effect of the given electrodes electric potential differences (inverse piezoeffect). The solution of the boundary-value problem of electroelasticity is also considered in the case of the direct piezoeffect when as a result of diffraction on the opening of monochromatic shear waves the generation of electric potential difference takes place on electrode coverings. An approximate scheme of numerical realization of the solvable system of singular integro-differential equations of the second kind with discontinuous kernels is given. There are presented some examples.

Mixed Antiplane Problem of Electroelasticity for a Piezoceramic Half-Space with a Tunnel Hole

Harmonic vibrations of a piezoceramic half-space weakened by a tunnel hole with a system of active surface electrodes are investigated. Based on integral representations for solutions to two types of conditions on the boundary of the half-space, the boundary-value problem of electroelasticity is reduced to a system of singular integrodifferential equations of the second kind. The results of parametric investigations characterizing the behavior of the electroelastic field components on the boundary and in the region of a piecewise-homogeneous half-space are presented.

The antiplane problem of electroelasticity for a cylinder with a tunnel crack excited by an arbitrary system of surface electrodes

The antiplane mixed boundary-value problem of electroelasticity of the oscillations of an infinite piezoceramic cylinder, weakened by a curvilinear tunnel crack, is considered. Using special integral representations of the solution, the boundary-value problem is reduced to a system of singular integro-differential equations of the second kind with discontinuous kernels. The results of a numerical realization of the algorithm, characterizing the amplitude-frequency characteristics of a piecewise-uniform cylinder and the behaviour of the components of the electroelastic field in the region and on the boundary of the cylinder under conditions of the inverse piezoelectric effect, are presented.

Antiplane Problem of Electroelasticity for a Hollow Piezoceramic Cylinder Excited by a System of Surface Electrodes

An antiplane mixed boundary-value problem of electroelasticity is considered for a hollow piezoceramic cylinder with an arbitrary system of active surface electrodes generating its harmonic vibrations. The problem is solved using a method elaborated earlier for investigating vibrations of a solid piezoceramic cylinder with a system of active surface electrodes. The scheme of numerical solution of the obtained singular integro-differential equations of the boundary-value problem is based on the quadrature method. Calculation results are presented that describe the amplitude-frequency characteristics of a hollow cylinder and the behavior of some mechanical and electric quantities both within the cylinder and on its boundary.

Fundamental Solutions of Electroelasticity Equations for a Piezoceramic Layer in R3

Coupled electroelastic fields in a piezoceramic layer under the action of force and electric sources are determined analytically. The Fourier coefficients of the displacement and electric potential vectors and of the stress tensor are expressed in terms of the Macdonald cylindrical functions in a closed form. The solutions obtained can be used to consider the boundary-value problems of electroelasticity for a piezoceramic layer with tunnel heterogeneities.

First Boundary Value Problem of Electroelasticity for a Transversally Isotropic Plane with Curvilinear Cuts

The first boundary value problem of electroelasticity for a transversally isotropic plane with curvilinear cuts is investigated. The solvability of a system of singular integral equations is proved by using the potential method and the theory of singular integral equations.

First Boundary Value Problem of Electroelasticity for a Transversally Isotropic Plane with Curvilinear Cuts

The first boundary value problem of electroelasticity for a transversally isotropic plane with curvilinear cuts is investigated. The solvability of a system of singular integral equations is proved by using the potential method and the theory of singular integral equations.

Concentration of electroelastic fields in a composite piezoceramic plate with defects crossing the interface

The characteristics of fracture and strength of a composite piezoceramic plate with defects in the form of cracks and holes situated in both of the plate components are investigated. The corresponding boundary-value problems of electroelasticity are reduced to systems of singular integral equations by constructing integral representations of the complex potentials. The results of numerical realization of the constructed algorithms are reported.

Extension of a piezoceramic bimorph with a crack crossing the interface

We consider the boundary-value problem of electroelasticity for a composite plate weakened by a crack crossing the line joining the media. The initial boundary-value problem, is reduced to a mixed system of singular integral and algebraic equations. We present the calculation results characterizing the variation in the stress intensity factors as a function of the opening angle of a segmented crack for different types of loading.

Boundary Value Problems of Electroelasticity with Concentrated Singularities

Abstract We investigate the solutions of boundary value problems of linear electroelasticity, having growth as a power function in the neighbourhood of infinity or in the neighbourhood of an isolated singular point. The number of linearly independent solutions of this type is established for homogeneous boundary value problems.