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1.
利用复变函数法、多极坐标及傅立叶级数展开技术求解了二维直角平面内固定圆形夹杂对稳态入射反平面剪切(shearing horizontal, SH)波的散射问题。首先构造出介质内不存在夹杂时的入射波场和反射波场,然后建立介质内存在夹杂时由夹杂边界产生的能够自动满足直角边应力自由条件的散射波解,从而利用叠加原理写出介质内的总波场。利用夹杂边界处位移条件和傅立叶级数展开方法列出求解散射波中未知系数的无穷代数方程组,在满足计算精度的前提下通过有限项截断,得到相应有限代数方程组的解,最后通过算例具体讨论了二维直角平面水平边界点的位移幅度比和相位随量纲一波数、入射波入射角及夹杂位置的不同而变化的情况,结果表明了算法的有效实用性。 相似文献
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利用复变函数法、多极坐标移动技术及傅立叶级数展开求解二维直角平面内圆形弹性夹杂对稳态入射平面SH波的散射问题。首先写出直角平面内不含夹杂时的入射波场和反射波场;其次建立直角平面内含夹杂时夹杂外的散射波解和夹杂内的驻波解,并利用叠加原理写出问题的总波场,借助夹杂边界处应力和位移的连续条件建立求解散射波解和驻波解中未知系数的无穷代数方程组并求解,通过算例具体讨论了直角平面水平边界点的位移幅度比和夹杂边界处径向应力集中系数随不同无量纲波数、入射角及圆孔位置的变化情况,结果表明了算法的有效实用性。 相似文献
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利用“Green函数法”和“镜像法”对垂直边界附近含圆孔的半空间双相压电介质对SH波的散射问题进行分析,得到其稳态解。利用镜像法得到满足水平边界应力自由与电位移自由的波函数解析表达式。根据垂直边界连续性条件,利用“契合法”建立第一类Fredholm型积分方程组,得到圆孔周边的动应力集中系数与电场强度集中系数解析表达式。数值算例分析了入射波频率、入射角度、介质参数等对动应力集中系数与电场强度集中系数的影响,并与已有文献进行比较。计算表明,高频SH波垂直入射危害较大。 相似文献
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采用复变函数法,结合"保角映射"技术及Green函数法,研究SH波作用下半空间内含有部分脱胶的椭圆夹杂以及圆形孔洞的散射问题。首先,利用"保角映射"技术将椭圆夹杂映射为圆夹杂,求出散射波位移场,同时,利用Green函数法与"虚设点源"的方法,求出半空间内椭圆夹杂以及圆孔的位移及应力场;然后,根据椭圆夹杂周围位移、应力连续、圆孔周围应力自由的边界条件,建立无穷线性代数方程组,求解出波函数中的未知系数;最后,在脱胶部分施加大小相等、方向相反的应力,构造出"脱胶模型",得到半空间内含有部分脱胶的椭圆夹杂以及圆形孔洞的总位移场。数值算例表明,入射角度、入射波频率、缺陷之间的距离、夹杂埋深及脱胶角度等对动应力集中因子有较大影响。 相似文献
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SH波入射时垂直半空间中双相介质界面附近圆孔的动力分析 总被引:2,自引:0,他引:2
利用复变函数和Green函数法研究了垂直半空间中双相介质界面附近圆孔对SH波的散射与动应力集中问题。该问题的解答采用镜像法,首先构造出含有圆孔的直角平面区域出平面问题的Green函数,然后利用契合技术,并根据界面处位移连续性条件将解答归结为具有弱奇异性的第一类Fredholm积分方程组的求解,结合散射波的衰减特性,直接离散该方程组,把积分方程组转化为线性代数方程组可得到该问题的数值结果。最后,通过算例分析了圆孔的动应力集中情况。结果表明,与全空间中界面附近圆孔对SH波的散射相比,由于垂直半空间自由边界的存在,孔边动应力集中系数明显增大;另外,入射波由硬介质(波速大)进入到软介质(波速小)时,与均匀介质相比,孔边动应力集中更显著,最不利的参数组合,孔边动应力集中系数几乎提高了一倍,入射波由软介质进入到硬介质时,情况相反。 相似文献
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Liu Diankui 《Acta Mechanica Sinica》1988,4(2):146-155
A new approach based on complex function to solve the SH-wave scattering problem around a circular hole in anisotropic media
is introduced in this paper. It is found that the dynamic stress concentration factor is dependent on the incident wave number
and the hole radius. Finally, some numerical results of dynamic stress concentration factor of a circular hole in anisotropic
media are given.
The Project Supported by National Natural Science Foundation of China 相似文献
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利用复变函数法和波函数展开法, 对地表软覆盖层中浅埋圆形夹杂在稳态SH波作用下的动应力集中问题进行研究并给出了解析解。根据SH波散射时的衰减特性, 采用了大圆弧假定的方法, 将半空间覆盖层直线边界问题转化为曲面边界问题。通过算例分析了SH波垂直入射时, 不同入射波波数和圆夹杂与半空间的波数比对圆形夹杂周边动应力集中因子的分布和动应力集中因子最大值变化的影响。算例表明, 圆形夹杂越“软”, 其波数越大, 夹杂周边的动应力集中因子越大; 入射波波数约0.35时, 夹杂周边的最大动应力集中因子达到最大值。
相似文献10.
Scattering of SH-waves by an interacting interface linear crack and a circular cavity near bimaterial interface 总被引:1,自引:0,他引:1
An analytical method is developed for scattering of SH-waves and dynamic stress concentration by an interacting interface crack and a circular cavity near bimaterial interface. A suitable Green‘s function is contructed, which is the fundamental solution of the displacement field for an elastic half space with a circular cavity impacted by an out-plane harmonic line source loading at the horizontal surface. First, the bimaterial media is divided into two parts along the horizontal interface, one is an elastic half space with a circular cavity and the other is a complete half space. Then the problem is solved according to the procedure of combination and by the Green‘s function method. The horizontal surfaces of the two half spaces are loaded with undetermined anti-plane forces in order to satisfy continuity conditions at the linking section, or with some forces to recover cracks by means of crack-division technique. A series of Fredholm integral equations of first kind for determining the unknown forces can be set up through continuity conditions as expressed in terms of the Green‘s function. Moreover, some expressions are given in this paper, such as dynamic stress intensity factor (DSIF) at the tip of the interface crack and dynamic stress concentration factor (DSCF) around the circular cavity edge. Numerical examples are provided to show the influences of the wave numbers, the geometrical location of the interface crack and the circular cavity, and parameter combinations of different media upon DSIF and DSCF. 相似文献
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Scattering of SH wave from an interface cylindrical elastic inclusion with a semicircular disconnected curve is investigated. The solution of dynamic stress concentration factor is given using the Green's function and the method of complex variable functions. First, the space is divided into upper and lower parts along the interface. In the lower half space, a suitable Green's function for the problem is constructed. It is an essential solution of the displacement field for an elastic half space with a semi-cylindrical hill of cylindrical elastic inclusion while bearing out-plane harmonic line source load at the horizontal surface. Thus, the semicircular disconnected curve can be constructed when the two parts are bonded and continuous on the interface loading the undetermined anti-plane forces on the horizontal surfaces. Also, the expressions of displacement and stress fields are obtained in this situation. Finally, examples and results of dynamic stress concentration factor are given. Influences of the cylindrical inclusion and the difference parameters of the two mediators are discussed. 相似文献
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Scattering of SH wave from an interface cylindrical elastic inclusion with a semicircular disconnected curve is investigated.The solution of dynamic stress concentration factor is given using the Gteen's function and the method of complex variable functions.First,the space is divided into upper and lower parts along the interface.In the lower half space,a suitable Green's function for the problem is constructed.It is an essential solution of the displacement field for an elastic half space with a semi-cylindrical hill of cylindrical elastic inclusion while bearing out-plane harmonic line source load at the horizontal surface.Thus,the semicircular disconnected curve can be constructed when the two parts are bonded and continuous on the interface loading the undetermined anti-plane forces on the horizontal surfaces.Also,the expressions of displacement and stress fields are obtained in this situation.Finally,examples and results of dynamic stress concentration factor are given.Influences of the cylindrical inclusion and the difierence parameters of the two mediators are discussed. 相似文献
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直角平面区域内固定圆形刚性夹杂问题的Green函数解 总被引:2,自引:0,他引:2
利用复变函数法、多极坐标移动技术研究了直角平面区域内含有固定圆形夹杂时的反平面问题Green函数解.首先构造出不含夹杂的完整直角平面区域内满足边界应力条件的入射位移场;其次,建立直角平面区域内固定圆形夹杂对该入射场产生的满足直角边界应力自由条件的散射波解,并由叠加原理得到介质内的总波场.最后利用夹杂边界处的位移条件确定出散射波解中的未知系数,最终得到问题的Green函数解,还通过算例讨论了夹杂边界处的径向应力和环向应力随不同波数、角度和不同夹杂位置及不同点源位置的变化情况.算例结果表明了该文方法的有效实用性. 相似文献
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研究了平面SH波在半空间双相弹性介质中的传播。通过Green函数和积分方程方法,按照复变函数描述,对透射波被圆孔散射的情况进行稳态分析。将双相介质半空间沿界面剖分为1/4空间介质Ⅰ和含圆孔的1/4空间介质Ⅱ,分别构造了介质Ⅰ和介质Ⅱ中反平面点源荷载的Green函数,按双相介质中平面SH波的处理方法,给出介质Ⅰ和介质Ⅱ中的平面位移波,两种介质之间的相互作用力与对应Green函数的乘积沿界面的积分与平面位移波叠加得到介质Ⅰ和介质Ⅱ中的全部位移场。按照界面的位移连续条件,定解积分方程组,得到问题的稳态解,并给出圆孔位置和介质参数对散射的影响。
相似文献17.
Scattering of SH-wave by cracks originating at an elliptic hole and dynamic stress intensity factor 总被引:1,自引:0,他引:1
The method of complex function and the method of Green‘s function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamicstress intensity factor at the crack tip was given. A Green‘s function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed. 相似文献
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SH波对双相介质界面附近圆形孔洞的散射 总被引:11,自引:1,他引:10
建立了求解平面SH波对双相介质界面附近圆形孔洞散射与动应力集中的一种分析方法.利用复变函数与多极坐标的方法构造了一个Green函数,它是在含有圆形孔洞的弹性半空间的水平面上任一点上作用时间谐和的出平面线源荷载的位移解.利用"契合"模型,并根据界面上位移连续性条件,建立了求解SH波对双相介质界面附近圆形孔洞散射的具有弱奇异性的第一类Fredholm型积分方程.给出了圆孔周边上动应力集中系数的表达式.作为算例,分析了在界面一侧或界面两侧附近具有圆形孔洞时SH波的散射,并讨论了入射波波数、不同的材料组合以及孔心至界面的距离对动应力集中的影响. 相似文献
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A system of equilibrium equations for nonthin transversely isotropic plates with a uniform prestress field is derived by expanding
the unknown functions into Fourier-Legendre series. A method of finding the general solution of this system is expounded and
used to determine the stress state of a plate with a circular cylindrical cavity
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 1, pp. 28–39, January 2008. 相似文献