Abstract: A torsional transient wave was assumed acting at infinity on the piezoelectric body
with an embedded penny-shaped crack. Appropriate governing equations and boundary conditions
have been built within the three-dimensional electroelasticity. The total displacement field was
simply considered as the combination of two parts, one related to incident waves inducing an
oscillating motion, and another with the scattered waves. An electric impermeable crack was
assumed to simplify the mathematical analysis. The problem was formulated in terms of integral
transforms techniques. Hankel transform were applied to obtain the dual integral equations, which
were then expressed to Fredholm integral equations of the second kind.

433

Authors: Xin Gang Li, Zhen Qing Wang, Nian Chun Lü

Abstract: The dynamic stress field under the SH-waves at the moving crack tip of functionally graded materials is analyzed, and the influences of parameters such as graded parameter, crack velocity, the angle of the incidence and the number of the waves on dynamic stress intensity factor are also studied. Due to the same time factor of scattering wave and incident wave, the scattering model of the crack tip can be constructed by making use of the displacement function of harmonic load in the infinite plane. The dual integral equation of moving crack problem subjected to SH-waves is obtained through Fourier transform with the help of the exponent model of the shear modulus and density, then have some process on the even and odd term of the integral kernel. The displacement is expanded into series form using Jacobi Polynomial, and then the semi-analytic and numerical solutions of dynamic stress intensity factor are derived with Schmidt method.

683

Authors: Wen Pu Shi, Cui Hua Li

Abstract: Several integrations of the plane wave functions frequently appearing in the scattering problems of elastic waves are considered in this study. In conjunction with the principle of superposition and the stationary wave function expansion, the exact solutions are obtained. As in the scattering problems of elastic waves and plane waves, the theoretical solutions can improve the convergence speed of the arithmetic and the computation precision. The analysis method and the analytical solutions can also be very helpful to solving other complex integrations in relation with the cylinder functions and plane functions.

2009

Authors: Li Li Sun, Tian Shu Song, Jian Liu

Abstract: Use the mirror method to transform the quarter space to the whole space under the complex coordinate system, and with the help of the boundary conditions around the cylindrical lining to solve the unknown coefficient. To do some numerical calculations of the dynamic stress concentration factor and the electric field intensity concentration factor around the cylindrical lining by using the program. In the numerical calculations stage, by changing the medium’s parameters, the structure’s geometry influence and the frequencies of incident wave to obtain more results on dynamic stress concentration factor (DSCF) and electric field intensity concentration factor (EFICF).The calculating results indicate that, under the action of SH wave the DSCF and EFICF around the cylindrical lining are similar to each other, and regularly distributed along the edge of the cylindrical lining. While the magnitude of DSCF and EFICF are larger than any other situations when the frequency of the incident wave was low. And the results are similar to results of the whole space condition too.

2179

Abstract: First we give the optical field function at distance z for a monochromatic light according to the Fresnel diffraction theory. The total optical field intensity is an integral of that of the monochromatic light. The total optical field intensity is not only related to the full width at half maximum, the distance, the structure of the serrated aperture, but also the radius of the ultrashort laser pulse. Numerical calculation shows that when the ratio of the averaged radius of the serrated aperture to the radius of the ultrashort laser pulse equals to 1 and the full width at half maximum is within a few tens of femtoseconds, the total optical field intensity reaches a constant along the axis direction and it is more stable than that without considering the radius of the ultrashort laser pulse in case that the Fresnel number of the laser pulse is about a hundred.

1085