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: Qing Yong Sun, Hong Yu Xu, Bin Liang

Abstract: Based on micropolar fluid theory and micropolar solid elasticity theory, reflection and transmission characteristics of three kinds of micropolar elastic waves, which are longitudinal displacement wave and two coupled waves, were studied when incident longitudinal displacement wave propagated in micropolar fluid with micropolar elastic plate. Using numerical example, the variations of various amplitudes are also shown against the angle of incidence and the variation characteristics of various amplitudes are discussed. Results show that there exist maximum values of reflection and transmission coefficient for coupled wave, however, there exist minimum values of reflection coefficient for longitudinal displacement wave, and transmission coefficient decreases with the incident angle and the transmission coefficient are smaller for bigger incident angle.

923

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

Abstract: This paper is devoted to so-called indirect discrete-continual boundary element method of structural analysis. Operational formulation of the problem is given. Using fundamental operational relations of indirect approach after construction of corresponding fundamental matrix-function in a special form convenient for problems of structural mechanics and its application resolving set of differential equations with operational coefficients is obtained. The discrete-continual design model for structures with constant physical and geometrical parameters in one direction is offered on the basis of so-called discrete-continual boundary elements. Basic pseudodifferential operators are approximated discretely by Fourier series. Fourier transformations and Wavelet analysis can be applied as well.

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