二维指数梯度弹性介质的格林函数

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-06-08 DOI:10.1098/rspa.2003.1220

Youn-Sha Chan, L. Gray, T. Kaplan, G. Paulino

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引用次数: 88

摘要

导出了二维指数梯度弹性介质的自由空间格林函数。假设剪切模量Âμ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为材料常数，泊松比为常数。格林函数由奇异部分(包含修正贝塞尔函数)和非奇异项组成。非奇异分量用一维傅里叶型积分表示，这种积分可以通过快速傅里叶变换计算得到。

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Green's function for a two–dimensional exponentially graded elastic medium

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.

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Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences

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