Green ’ s function for a two - dimensional exponentially graded elastic medium
نویسندگان
چکیده
The free-space Green function for a two-dimensional exponentially graded elastic medium is derived. The shear modulus μ is assumed to be an exponential function of the Cartesian coordinates (x, y), i.e. μ ≡ μ(x, y) = μ0e12, 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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