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Dynamic response of an isotropic elastic half-plane with shear modulus varying with depth to a load moving on its surface
Highlights Analytical solution of the moving load on a half-plane soil medium with shear modulus varying with depth. Complex Fourier series method in conjunction with the Frobenius method are utilizedfor the solution. Non-homogeneity index and gradient constant simulate different cases of shear modulus variation with depth. Increasing values of velocity result in increasing values of maximum vertical displacement.
Abstract The dynamic response of a half-plane soil medium to a load moving on its surface is obtained analytically-numerically. The soil is assumed to be linear elastic, isotropic and continuously non-homogeneous with its shear modulus varying with depth. Both cases of the shear modulus increasing and decreasing with depth are considered. The load is assumed to be distributed and moves with constant speed. The load and the soil displacements are expanded in complex Fourier series with respect to the horizontal direction x and the time t and thus the partial differential equations governing the soil motion are reduced to ordinary differential equations with variable coefficients, which are solved analytically by the method of Frobenius. The correctness of the solution in series form is checked by using it to solve some special case problems for which there exist closed form solutions in the literature. Parametric studies are conducted to assess the effect of non-homogeneity on the response for both cases of the shear modulus increasing and decreasing with depth.
Dynamic response of an isotropic elastic half-plane with shear modulus varying with depth to a load moving on its surface
Highlights Analytical solution of the moving load on a half-plane soil medium with shear modulus varying with depth. Complex Fourier series method in conjunction with the Frobenius method are utilizedfor the solution. Non-homogeneity index and gradient constant simulate different cases of shear modulus variation with depth. Increasing values of velocity result in increasing values of maximum vertical displacement.
Abstract The dynamic response of a half-plane soil medium to a load moving on its surface is obtained analytically-numerically. The soil is assumed to be linear elastic, isotropic and continuously non-homogeneous with its shear modulus varying with depth. Both cases of the shear modulus increasing and decreasing with depth are considered. The load is assumed to be distributed and moves with constant speed. The load and the soil displacements are expanded in complex Fourier series with respect to the horizontal direction x and the time t and thus the partial differential equations governing the soil motion are reduced to ordinary differential equations with variable coefficients, which are solved analytically by the method of Frobenius. The correctness of the solution in series form is checked by using it to solve some special case problems for which there exist closed form solutions in the literature. Parametric studies are conducted to assess the effect of non-homogeneity on the response for both cases of the shear modulus increasing and decreasing with depth.
Dynamic response of an isotropic elastic half-plane with shear modulus varying with depth to a load moving on its surface
Muho, Edmond V. (author) / Beskou, Niki D. (author)
2019-05-29
Article (Journal)
Electronic Resource
English
| Taylor & Francis Verlag | 2023
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