This paper describes the effects of soil non-homogeneity, the soil–structure interaction and the two-parameter elastic foundation model on the free vibration of Euler–Bernoulli beams. Non-homogeneity of the soil foundation is described by parabolic variations of the two-parameter elastic soil foundation while Poisson's ratio is assumed to remain constant. Hence, the soil–structure interaction is quantified using a relative ratio of beam and soil foundation properties. The equation of motion including the previous effects is derived and the fundamental frequency parameters are computed. The influence of the above parameters on the free-vibration characteristics of the beam is investigated. The results obtained from this analytical method for a simply supported beam were found to be in very good agreement with data from the literature.

中文翻译：

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土壤非均质性与结构相互作用对梁振动的影响

本文描述了土的非均质性，土-结构的相互作用以及两参数弹性地基模型对欧拉-伯努利梁自由振动的影响。用两参数弹性土壤基础的抛物线变化描述了土壤基础的非均质性，而泊松比则保持不变。因此，利用梁和土壤基础特性的相对比率来量化土壤与结构的相互作用。推导包括先前效应的运动方程，并计算基本频率参数。研究了以上参数对梁自由振动特性的影响。通过这种分析方法获得的简单支撑梁的结果与文献数据非常吻合。