This paper presents an analytical method for modeling the dynamic response of a rigid strip footing subjected to vertical‐only loads. The footing is assumed to rest on the surface of a viscoelastic half‐space; therefore, effects of hysteretic soil damping on the impedance of the foundation and the generated ground vibrations are considered in the solution. To solve the mixed boundary value problem, we use the Fourier transform to cast a pair of dual integral equations providing contact stresses, which are solved by means of Jacobi orthogonal polynomials. The resulting soil and footing displacements and stresses are obtained by means of the Fourier inverse transform. The solution provides more realistic estimates of footing impedance, compared to existing solutions for elastic soil, as well as of the attenuation of ground vibrations with distance of the footing. The latter is important for the estimation of machine vibration effects on nearby structures and installations.

中文翻译：

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刚性条形基础在粘弹性半空间上的垂直振动

本文提出了一种分析方法，用于建模仅承受垂直载荷的刚性带状基础的动力响应。假定立足点位于粘弹性半空间的表面上。因此，在解决方案中考虑了滞后土壤阻尼对地基阻抗和产生的地面振动的影响。为了解决混合边值问题，我们使用傅立叶变换来铸造一对提供接触应力的对偶积分方程，并通过雅可比正交多项式对其进行求解。通过傅立叶逆变换获得所得的土壤和基础位移和应力。与现有的弹性土壤解决方案相比，该解决方案提供了更为实用的基础阻抗估算值，以及随着立脚距离的增加，地面振动的衰减。后者对于估计机器振动对附近结构和装置的影响很重要。