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TRANSVERSE MODES IN PHASE-CONJUGATION RESONATOR(PCR) WITH FINITE APERTUREA(Ⅰ)——MATRIX eigen-equation OF SELF-CONSISTENT FIELD

引用

Science China Mathematics 1990年第8期33卷 982-995页

作者：李先枢徐家进高燕球 Department of Physics Zhongshan University Guangzhou 510275 PRC Department of Physics Guangzhou Teacher's College Guangzhou 510400 PRC

Based on "the matrix theory for the propagation of a scalar light wave in a system consisting of plane screens （cylindrical coordinates）" proposed by one of the authors （1981）, the propagation of the self-consistent field in PCR is analyzed, and a matrix eigen-equation of the self-consistent field is presented. By solving the eigen-equation, the axisymmetrical PCR with finite aperture is calculated, and the diffraction losses, phase shifts, relative amplitude and phase distributions on each mirror surface of various order transverse modes （including high-order modes, whose l≥2, p≥1） are introduced.A quasi-equivalence relation of PCR is also given. According to this relation, some characteristics （as the diffraction loss, the field distribution on the surface of spherical mirror） of all transverse modes in a PCR are just the same as those in some of the other PCR with different g1.Some examples of calculation results are also given. They show that （ⅰ） the convengence of the above-mentioned equation

关键词： phase conjugation resonator transverse mode matrix eigen-equation of self-eonsistent field matrix theory for the propagation of scalar light wave quasiequivalence relation.

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METHOD TO CALCULATE STRESS INTENSITY FACTOR OF V-NOTCH IN BI-MATERIALS

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Acta Mechanica Solida Sinica 2008年第4期21卷 337-346页

作者： Youtang Li Ming Song Key Laboratory of Digital Manufacturing Technology and Application Ministry of Education Lanzhou University of Technology Lanzhou 730050 China College of Meehano-Electronic Engineering Lanzhou University of Technology Lanzhou 730050 China

Based on Zak＇s stress function, the eigen-equation of stress singularity ofbi-materials with a V-notch was obtained. A new definition of stress intensity factor for a perpendicular interfacial V-notch of bi-material was put forward. The effects of shear modulus and Poisson＇s ratio of the matrix material and attaching material on eigen-values were analyzed. A generalized expression for calculating/（i of the perpendicular V-notch of bi-materials was obtained by means of stress extrapolation. Effects of notch depth, notch angle and Poisson＇s ratio of materials on the singular stress field near the tip of the V-notch were analyzed systematically with numerical simulations. As an example, a finite plate with double edge notches under uniaxial uniform tension was calculated by the method presented and the influence of the notch angle and Poisson＇s ratio on the stress singularity near the tip of notch was obtained.

关键词： bi-material V-notch eigen-equation stress intensity factor finite element method

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