Piezoelectric Material Strip Research Articles

A Normal Crack in a Piezoelectric Actuator with Functionally Graded Properties under a Transient Thermal Load Combined with an Electric Load

In this paper, the fracture problem of a piezoelectric actuator consisting of a functionally graded piezoelectric material strip (FGPM strip) and a homogeneous layer by a transient thermal load combined with an electric load is considered. The FGPM strip contains a crack perpendicular to the interface. Material properties of the FGPM strip are assumed to be exponentially dependent on the distance from the interface. The thermo-electro-mechanical fields in the un-cracked laminate induced by the transient thermal load and the electric load are calculated. By using the superposition technique, the obtained normal stresses are used as the crack surface tractions with opposite sign to formulate the mixed boundary value problem. The integral transform techniques are employed to reduce the problem to the solution of a singular integral equation. The stress intensity factors are computed, and the results are presented for the various values of the nonhomogeneous and geometric parameters. We also focused on the crack contact phenomenon for the case of the pure electric load. Moreover, the effect of the difference between two kinds of the electric boundary conditions on the stress intensity factors under transient thermal load and the reduction of ones by the electric load would be discussed.

Dynamic response of a cracked thermopiezoelectric strip under thermoelectric loading using fractional heat conduction

This study is concerned with the dynamic behavior of a piezoelectric material strip with a parallel crack under thermal shock and transient electric loading. The governing thermal and electromechanical equations are exactly reduced to a system of Cauchy-type singular integral equations by applying Laplace and Fourier transforms and the dislocation density functions. Numerical examples are discussed in detail to show the effects of the applied heat conduction model, cracked strip configuration, and electrical load variables on the dynamic thermal results and the stress-electric displacement intensity factors. The results reveal that the overshooting phenomenon would be more evident with the longer relaxation time and higher fractional order, while the wave behavior becomes weaker and stronger, respectively. There are apparent inflection points on the dynamic stress intensity factors (DSIFs) and the dynamic electric displacement intensity factor (DEDF) curves for different configurations of the strip and the coefficients of the heat conduction model. In addition, the stress intensity factors are insensitive to the electric load which has a dominant influence on the electric displacement intensity factor.

Singular electro-elastic fields at the tip of the crack normal to the interface between a functionally graded piezoelectric material strip and a homogeneous elastic layer induced by an electric load

Singular electro-elastic fields at the tip of the crack normal to the interface between a functionally graded piezoelectric material strip and a homogeneous elastic layer induced by an electric load

Singular electro-elastic fields at the tip of the crack normal to the interface between a functionally graded piezoelectric material strip and a homogeneous elastic layer induced by an electric load

Singular electro-elastic fields at the tip of the crack normal to the interface between a functionally graded piezoelectric material strip and a homogeneous elastic layer induced by an electric load

The dynamic stress analysis of an infinite piezoelectric material strip with a circular cavity

The scattering of SH guided wave by a circular cavity in an infinite piezoelectric material strip is analyzed by using “mirror image method” and guided wave theory, and the analytical expressions of guided wave function satisfying stress free and electric insulation conditions on the upper and lower horizontal boundaries of the strip domain are obtained. The analytical expression of the scattered wave around a circular cavity is constructed by using the method of multiple mirror superposition and wave function expansion. The integral equations are established and solved by the boundary conditions of the circular cavity, and the analytical expressions of the dynamic stress concentration factor and the electric field intensity factor are obtained. The effects of incident wave frequency, dielectric parameters and circular cavity position on electric field intensity concentration factor (EFICF) and dynamic stress concentration factor (DSCF) are analyzed by numerical examples. Besides, the analytical solutions obtained in this article are compared with the finite element solutions and the analytical solutions in previous literature to verify the correctness and accuracy of the conclusions in this article. And the conclusions in this article are of great reference value to the selection and ultrasonic nondestructive testing of anti-seismic materials.

Anti-plane crack problem of a functionally graded piezoelectric materials strip with arbitrarily distributed properties

This paper treats the anti-plane crack problem of a functionally graded piezoelectric material (FGPM) strip with arbitrarily distributed properties. It is assumed that the elastic stiffness, piezoelectric constant, and dielectric constant of the FGPM vary continuously along the thickness of the medium, and the strip is under anti-plane mechanical and in-plane electric impact loadings. By using the Fourier transform and defining unknown discontinuous functions across the crack surfaces, the anti-plane crack problem of FGPM is reduced to a group of singular integral equations, which are solved numerically. The stress and electric displacement intensity factors are presented, and the influences of the nonhomogeneous and geometric parameters on stress and electric displacement intensity factors are also included.

Scattering of SH guided wave by a circular inclusion and semicircular depression in an infinite piezoelectric material strip

ABSTRACT By means of the guided wave theory, the scattering of SH guided wave by a circular inclusion and semicircular depression in an infinite piezoelectric material strip is investigated. The multi-polar coordinate change method is used to deal with semicircular sag at the boundary position. By using the method of multiple images, the theoretical expressions of scattering waves, satisfying the stress-free and electrical insulation conditions at the upper and lower boundaries of the band domain, are constructed. Based on the boundary conditions, the integral equations are established. The analytical expressions of the dynamic stress concentration coefficient and electric field intensity concentration coefficient are obtained. By analyzing the order of the guided wave, the physical parameters of the medium, the distance between the center of a circular inclusion, the location of a semicircular depression and a circular inclusion and the radius of the semicircular depression, the dynamic stress concentration factor and electric field intensity concentration factor are analyzed and compared with the existing literature in calculating example.

Transient thermal response of functionally graded piezoelectric laminates with an infinite row of parallel cracks normal to the bimaterial interface

In this paper, the problem of a functionally graded piezoelectric material strip (FGPM strip) containing an infinite row of parallel cracks perpendicular to the interface between the FGPM strip and a homogeneous layer is analyzed under transient thermal loading condition. The crack faces are supposed to be completely insulated. Material properties are assumed to be exponentially dependent on the distance from the interface. Using the Fourier transforms, the electro-thermoelastic problem is reduced to a singular integral equation, which is solved numerically. The stress intensity factors are computed and presented as a function of the normalized time, the nonhomogeneous and geometric parameters.

Scattering of SH guided wave by a circular inclusion in an infinite piezoelectric material strip

By the means of the guided wave theory, the scattering of SH guided wave by a circular inclusion in an infinite piezoelectric material strip is investigated. With the aid of repeated image superposition, the analytical expression of scattering wave is conducted, which satisfies the stress free and electric insulation conditions on the upper and lower horizontal boundaries of the strip. According to the boundary condition, integral equation is set up and analytical expression of dynamic stress concentration factor and electric field intensity concentration factor are obtained. The influence of the order of guided waves, the physical parameters of the medium and position of the circular inclusion on the dynamic stress concentration factor and electric field intensity concentration factor are analyzed and compared with the existing literature in calculating example.

Transient thermal response of a functionally graded piezoelectric laminate with a crack normal to the bimaterial interface

ABSTRACTIn this article, the problem of a functionally graded piezoelectric material strip (FGPM strip) containing a crack perpendicular to the interface between the FGPM strip and a homogeneous layer is analyzed under transient thermal loading condition. The crack faces are supposed to be completely insulated. Material properties are assumed to be exponentially dependent on the distance from the interface. Using the Laplace and Fourier transforms, the thermoelectromechanical problem is reduced to a singular integral equation, which is solved numerically. The stress intensity factors of embedded and edge cracks are computed. The results for the crack contact problem are also included.

Transient thermoelectroelastic response of a piezoelectric material strip with two parallel cracks in arbitrary positions

ABSTRACTThis work is concerned with the thermoelectromechanical fracture behavior of two parallel cracks in arbitrary positions of a piezoelectric material strip under thermal shock loading. The crack faces are supposed to be insulated thermally and electrically. By using both the Laplace transform and the Fourier transform, the thermal and electromechanical problems are reduced to two systems of singular integral equations. The singular integral equations are solved numerically, and a numerical method is then employed to obtain the time-dependent solutions by way of a Laplace inversion technique. The intensity factors versus time for various geometric parameters are calculated and presented in graphical forms. The temperature, stress and electric displacement distributions in a transient state are also included.

Transient Thermoelectroelastic Response of a Functionally Graded Piezoelectric Material Strip with Two Parallel Cracks in Arbitrary Positions

In this article, the problem of two parallel cracks in arbitrary positions of a functionally graded piezoelectric material (FGPM) strip is analyzed under transient thermal loading conditions. It is assumed that the thermoelectroelastic properties of the strip vary continuously along the thickness of the strip, and that the crack faces are supposed to be insulated thermally and electrically. By using both the Laplace transform and the Fourier transform, the thermal and electromechanical problems are reduced to two systems of singular integral equations. The singular integral equations are solved numerically, and a numerical method is then employed to obtain the time dependent solutions by way of a Laplace inversion technique. The intensity factors versus time for various geometric and material parameters are calculated and presented in graphical forms. Temperature change, the stress and electric displacement distributions in a transient state are also included.

OS1301 任意位置に平行二き裂を有する傾斜機能圧電厚板の電気熱弾性応答

OS1301 任意位置に平行二き裂を有する傾斜機能圧電厚板の電気熱弾性応答

Evaluation by the stress intensity factor of two coplanar cracks in a piezoelectric strip under mechanical and transient thermal loadings

In this paper, the fracture problem of a piezoelectric material strip containing two coplanar cracks perpendicular to its boundaries is considered. The problem is solved for a strip that is suddenly heated from both the top and the bottom surfaces under static mechanical loading. In spite of many studies in the thermo-electro-mechanical fracture problem of a piezoelectric material strip with a crack, not much work has been done in the context of the crack contact problem. The main object of this paper is also to study the crack contact problem. By using the Fourier transform, the thermoelectromechanical fracture problem is reduced to a system of singular integral equations, which are solved numerically. The numerical results for the stress and thermal stress intensity factors are computed as a function of the normalized time and geometric parameters. For the cases of two embedded cracks and an embedded crack and an edge crack, the effect of the upper crack geometry on the fracture behavior of the lower crack are considered under the pure mechanical load and the pure thermal load, respectively. The following facts can be found from the numerical results. First, the stress intensity factor of lower edge crack under pure mechanical load monotonically decreases with increasing the upper embedded crack length. Second, absolute value of the stress intensity factor of inner crack tip under the pure thermal load increases with increasing the heating temperature. Finally, taking the crack contact into consideration, it is found that the edge crack in the strip under the heating process would be fully closed at some time after the thermal shock.

Transient Thermoelectroelastic Response of a Functionally Graded Piezoelectric Strip with Two Parallel Axisymmetric Cracks

In this article, the problem of two parallel axisymmetric cracks in a plate of a functionally graded piezoelectric material (FGPM) strip is analyzed under transient thermal loading conditions. It is assumed that the thermoelectroelastic properties of the strip vary continuously along the thickness of the strip, and that the crack faces are supposed to be insulated thermally and electrically. By using both the Laplace and Hankel transforms, the thermal and electromechanical problems are reduced to two systems of singular integral equations. The singular integral equations are solved numerically, and a numerical method is then employed to obtain the time dependent solutions by way of a Laplace inversion technique. Systematic numerical calculations are carried out, and the field intensity factors versus time are presented for various values of dimensionless parameters representing the crack geometry and the material non-homogeneity.

Two Parallel Cracks in Arbitrary Positions of a Piezoelectric Material Strip Under Thermo-Electric Loadings

In this article, thermo-electro-elastic fracture behavior of two parallel cracks in arbitrary positions of a piezoelectric material strip under thermo-electric loadings is considered. The crack faces are assumed to be insulated thermally and electrically. Fourier transform techniques are used to reduce the mixed boundary value problems to two systems of singular integral equations. Numerical calculations are carried out, and detailed results are presented to illustrate the influence of the geometric parameters on the stress and electric displacement intensity factors. The results for the temperature and electro-elastic fields are also included.

OS0821 任意位置に平行二き裂を有する圧電厚板の電気熱弾性応答

OS0821 任意位置に平行二き裂を有する圧電厚板の電気熱弾性応答

Two coplanar cracks in a functionally graded piezoelectric material strip under mechanical and transient thermal loadings

In this paper, the fracture problem of a functionally graded piezoelectric material strip (FGPM strip) containing two coplanar cracks perpendicular to its boundaries is considered. The problem is solved for an FGPM strip that is suddenly heated from the bottom surface under static mechanical loading. The top surface is maintained at the initial temperature. The crack faces are supposed to be completely insulated. Material properties are assumed to be exponentially dependent on the distance from the bottom surface. By using the Laplace and Fourier transforms, the thermoelectromechanical fracture problem is reduced to a set of singular integral equations, which are solved numerically. The stress intensity factors for the cases of the two embedded cracks, two edge cracks, and an embedded crack and an edge crack are computed and presented as a function of the normalized time, the nonhomogeneous and geometric parameters.

Transient Thermoelectromechanical Response of a Piezoelectric Strip with Two Parallel Cracks of Different Lengths

This work is concerned with the thermoelectromechanical fracture behavior of two parallel cracks of different lengths in a piezoelectric material strip under thermal shock loading. The crack faces are supposed to be insulated thermally and electrically. By using both the Laplace transform and the Fourier transform, the thermal and electromechanical problems are reduced to two systems of singular integral equations, respectively, which are solved numerically. A numerical method is employed to obtain the time dependent solutions by way of a Laplace inversion technique. The intensity factors versus time for various geometric parameters are calculated and presented in graphical forms. Temperature change, the stress and electric displacement distributions in a transient state are also included.

Normal Cracks in a Functionally Graded Piezoelectric Material Strip Under Transient Thermal Loading

Piezoelectric materials widely have been used as sensors and actuators in smart or intelligent systems to sense thermally induced distortions and to adjust for adverse thermomechanical conditions. The requirements of structural strength, reliability and lifetime of these structures call for a better understanding of the mechanics of fracture in piezoelectric materials under thermal loading. In this paper, the fracture problem of a functionally graded piezoelectric material strip (FGPM strip) containing two cracks (coplanar cracks) perpendicular to its boundaries is considered. The problem is solved for an FGPM strip that is suddenly heated from the bottom surface. The top surface is maintained at the initial temperature. The crack faces are supposed to be completely insulated. Material properties are assumed to be exponentially dependent on the distance from the bottom surface. By using the Laplace and Fourier transforms, the thermoelectromechanical fracture problem is reduced to a set of singular integral equations, which are solved numerically. The stress intensity factors for the cases of the single crack, the two embedded cracks, two edge cracks, and an embedded and an edge cracks are computed and presented as a function of the normalized time, the nonhomogeneous and geometric parameters.