Dynamic response of a gradient elastic half-space to a load moving on its surface with constant speed
| Autor: | Ying Zhou, S. Papargyri-Beskou, Edmond V. Muho, I. P. Pegios |
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| Rok vydání: | 2021 |
| Předmět: |
Physics
Partial differential equation Mechanical Engineering Mathematical analysis Computational Mechanics Moving load 02 engineering and technology Half-space Granular material 01 natural sciences 010305 fluids & plasmas 020303 mechanical engineering & transports 0203 mechanical engineering Ordinary differential equation 0103 physical sciences Boundary value problem Constant (mathematics) Fourier series |
| Zdroj: | Acta Mechanica. 232:3159-3178 |
| ISSN: | 1619-6937 0001-5970 |
| DOI: | 10.1007/s00707-021-03003-7 |
| Popis: | The problem of determining the dynamic response of a granular elastic half-space soil medium to a rectangular load moving on its surface is determined analytically. The granular material is modeled as a gradient elastic solid with two material constants in addition to the two classical elastic moduli. These material constants with dimensions of length are the micro-stiffness g and the micro-inertia h coefficients. The rectangular load is uniformly distributed of constant magnitude and moves with constant speed. The resulting three partial differential equations of motion are of the fourth order with respect to the horizontal x, y, and vertical z coordinates and of second order with respect to time t. These equations are solved with the aid of double complex Fourier series involving x, y, t, and the load velocity, which reduce them to a system of three ordinary differential equations of the fourth order with respect to z, which can be easily solved. Use of appropriate classical and non-classical boundary conditions can lead to the solution of the problem. The so obtained solution is used to easily assess by parametric studies the effects of the microstructural parameters g and h as well as the moving load velocity on the various response quantities. |
| Databáze: | OpenAIRE |
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