Green's function for a two–dimensional exponentially graded elastic medium
Green's function for a two–dimensional exponentially graded elastic medium
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DOI：
10.1098/rspa.2003.1220
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发表时间：
2004-06
期刊：
影响因子：
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通讯作者：
Youn-Sha Chan;L. Gray;T. Kaplan;G. Paulino
中科院分区：
文献类型：
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作者：
Youn-Sha Chan;L. Gray;T. Kaplan;G. Paulino
导出了二维指数梯度弹性介质自由空间的绿色函数。假设剪切模量μ是笛卡尔坐标（x，y）的指数函数，即μ ∈ μ（x，y）= μ0e2（β1x+β2y），其中μ0，β1和β2是材料常数，泊松比假设为常数。示出的绿色功能，包括一个奇异的部分，涉及修改贝塞尔函数，和一个非奇异项。非奇异分量表示在一维傅里叶型积分，可以计算的快速傅里叶变换。
The free–space Green function for a two–dimensional exponentially graded elastic medium is derived. The shear modulus Âμ is assumed to be an exponential function of the Cartesian coordinates (x,y), i.e. μ ≡ μ(x,y) = μ0e2(β1x+β2y), where μ0, β1, and β2 are material constants, and the Poisson ratio is assumed constant. The Green function is shown to consist of a singular part, involving modified Bessel functions, and a non–singular term. The non–singular component is expressed in terms of one–dimensional Fourier–type integrals that can be computed by the fast Fourier transform.