Y. Shindo

Singular stress and electric fields of a piezoelectric ceramic strip with a finite crack under longitudinal shear

SummaryFollowing the theory of linear piezoelectricity, we consider the problem of determining the singular stress and electric fields in an orthotropic piezoelectric ceramic strip containing a Griffith crack under longitudinal shear. The crack is situated symmetrically and oriented in a direction parallel to the edges of the strip. Fourier transforms are used to reduce the problem to the solution of a pair of dual integral equations. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. Numerical values on the stress intensity factor and the energy release rate for piezoelectric ceramics are obtained, and the results are graphed to display the influence of the electric field.

Electroelastic intensification near anti-plane shear crack in orthotropic piezoelectric ceramic strip

Abstract The theory of linear piezoelectricity is applied to solve the antiplane electroelastic problem of an orthotropic piezoelectric ceramic strip with a finite crack, which is situated symmetrically and oriented in a direction normal to the edges of the strip. Fourier transforms are used to reduce the problem to the solution of a pair of dual integral equations. They are then reduced to a Fredholm integral equation of the second kind. Numerical values on the stress intensity factor and the energy release rate for some piezoelectric ceramics are obtained and the results are displayed numerically to exhibit the electroelastic interactions.

Dynamic stress intensity factor of a cracked dielectric medium in a uniform electric field

SummaryWe consider the scattering of normally incident longitudinal waves by a finite crack in an infinite isotropic dielectric body under a uniform electric field. By the use of Fourier transforms, we reduce the problem to that of solving two simultaneous dual integral equations. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind having the kernel that is a finite integral. The dynamic stress intensity factor versus frequency is computed, and the influence of the electric field on the normalized values is displayed graphically.

Electroelastic analysis of piezoelectric ceramics with surface electrodes

Following the theory of liner piezoelectricity, we consider the static behavior of the elastic and electric variables in the vicinity of a surface electrode attached to a piezoelectric ceramic. Fourier transforms are used to reduce the mixed boundary value problem to the solution of a pair of dual integral equations. The integral equations are solved exactly and the displacement and electric potential are expressed in closed form.

Impact response of a finite crack in an orthotropic piezoelectric ceramic

SummaryThe transient dynamic stress intensity factor and dynamic energy release rate were determined for a cracked piezoelectric ceramic under normal impact in this study. A plane step pulse strikes the crack and stress wave diffraction takes place. Laplace and Fourier transforms are employed to reduce the transient problem to the solution of a pair of dual integral equations in the Laplace transform plane. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. A numerical Laplace inversion technique is used to compute the values of the dynamic stress intensity factor and the dynamic energy release rate for some piezoelectric ceramics, and the results are graphed to display the electroelastic interactions.

Dynamic bending of a symmetric piezoelectric laminated plate with a through crack

The dynamic theory of linear piezoelectricity is applied to analyze the scattering of time harmonic flexural waves by a through crack in a symmetric piezoelectric laminated plate subjected to electric field loading. An incident wave giving rise to moments symmetric about the crack plane is considered. Piezoelectric layers are added to the upper and lower surfaces. Classical lamination theory is extended to include dynamic piezoelectric effects. Fourier transforms are used to reduce the problem to the solution of a pair of dual integral equations, the solution of which is then expressed in terms of a Fredholm integral equation of the second kind. The dynamic moment intensity factor vs. frequency is computed and the influence of the electric field on the normalized values is displayed graphically.

Anti-plane shear crack growth rate of piezoelectric ceramic body with finite width

Abstract The theory of linear piezoelectricity is applied to develop an anti-plane crack growth rate equation of a finite crack in a piezoelectric ceramic body with finite width. Plastic zone is assumed to be confined to a sheet ahead of both crack edges similar to the strip model for in-plane loading. The procedure consists of reducing a system of dual integral equations to a Fredholm integral equation of the second kind. The accumulated plastic displacement criterion is used for developing a solution for the crack growth rate. Numerical values of crack growth rate are obtained and the results are displayed graphically to exhibit the electroelastic interactions.

Magneto-elastic analysis of a soft ferromagnetic plate with a through crack under bending

Following a classical plate bending theory of magneto-elasticity, we consider the crack problem of a soft ferromagnetic plate under a uniform magnetic field. By the use of Fourier transforms we reduce the problem to solving a pair of dual integral equations. The solution of the dual integral equations is then expressed in terms of a Fredholm integral of the second kind. The bending moment intensity factor is computed and the influence of the magnetic field on the normalized values is displayed graphically.

Flexural Wave Scattering at a Through Crack in a Conducting Plate Under a Uniform Magnetic Field

Following a classical plate bending theory of magneto-elasticity, we consider the scattering of time-harmonic flexural waves by a through crack in a conducting plate under a uniform magnetic field normal to the crack surface. An incident wave giving rise to moments symmetric about the crack plane is applied. It is assumed that the plate has the electric and magnetic permeabilities of the free space. By the use of Fourier transforms we reduce the problem to solving a pair ofdual integral equations. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. The dynamic moment intensity factor versus frequency is computed and the influence of the magnetic field on the normalized values is displayed graphically. It is found that the existence of the magnetic field produces higher singular moments near the crack tip.

Scattering of oblique flexural waves by a through crack in a conducting mindlin plate in a uniform magnetic field

This paper deals with the scattering of time harmonic flexural waves by a through crack in a conducting plate under a uniform magnetic field normal to the crack surface. This study is based on Mindlins theory of plate bending for magneto-elastic interactions under a quasistatic electromagnetic field. It is assumed that the plate has finite and electric conductivity, and the electric and magnetic permeabilities of free space. An incident wave giving rise to moments symmetric about the crack plane is applied in an arbitrary direction. Fourier transforms are used to reduce the mixed boundary value problem to one involving the numerical solution of Fredholm integral equations. The dynamic moment intensity factor vs frequency is computed and the influence of the magnetic field and the angle of incidence on the normalized values is displayed graphically.