与波函数相关的几个积分的理论解  

THEORETICAL SOLUTIONS OF SEVERAL INTEGRATIONS IN RELATION WITH THE WAVE FUNCTIONS

作　　者：段彩云[1] 史文谱[2,3] 于涛[2,3] 

机构地区：[1]山东商务职业学院机械工程系,烟台264005 [2]烟台大学机电汽车工程学院,烟台264005 [3]山东省高校先进制造及控制技术重点实验室,烟台264005

出　　处：《机械强度》2012年第4期562-567,共6页Journal of Mechanical Strength

基　　金：山东省自然科学基金(ZR2010AM002);山东省科技攻关项目(2006GG3210001)资助~~

摘　　要：利用傅里叶级数展开技术、平面波驻波展开式和Graf加法公式分析求解稳态P(primary wave)波、SV(shearing vertical)波和SH(shearing horizontal)波散射问题中大量出现的与平面波和散射波函数有关的复杂积分,这些积分理论解避免了数值积分中常出现的收敛速度慢、计算量大、计算精度低的现象,可为编制高效率、高可靠性的弹性波散射计算软件提供理论依据和结果。Fourier series expansion technology, standing wave expansion of the plane wave and Graf addition formula were used to deal with the complex integrations of the plane wave functions and scattering wave functions frequently appearing in the scattering problems about P-waves and SV-waves and SH-waves. These integration theoretical solutions can avoid the phenomena of low convergence speed, large computation and low computation precision often appearing in numerical integration computation, they can supply theoretical bases and results for programming high efficient, reliable computing software of elastic wave scattering.

关 键 词：弹性波散射 波函数积分 平面波的驻波展开Graf加法公式 

分 类 号：O347.41[理学—固体力学]