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New Semi-analytical Solution for a Moving Mass Problem: the Effect of Initial Conditions and Abrupt Change in Foundation Stiffness

机译：移动质量问题的新半分析解决方案：初始条件和突变变化基础刚度的影响

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In this contribution, the new semi-analytical solution for the moving mass problem from [1] is extended to account for the influence of initial conditions. The essential part of the new closed-form formula derived in [1] is the term governed by the mass-induced frequencies, which cannot be obtained when a common solution method for this kind of problems like double Fourier transform is used. Apart the term given by the closed-form formula, there is a transient part of natural vibrations originated by a line discontinuity in the Laplace image of the displacement under the load. Analytical expression is derived for such a defined line cut. Then the transient part is determined by numerical integration and added to the response given by the closed-form formula. Very good coincidence between results on finite and infinite beams is obtained, which is further exploited for the analysis of the influence of the abrupt change in the foundation stiffness.
机译：在这一贡献中，从[1]的移动质量问题的新半分析解决方案延伸到算用于初始条件的影响。在[1]中衍生的新闭合形式公式的基本部分是由质量诱导的频率控制的术语，当使用像双傅里叶变换等类型问题的常见解决方法时，不能获得。除闭合形式公式中的术语分开，源自自然振动的瞬态部分起源于负载下位移的拉普拉斯映像中的线路不连续。用于这种定义的线切割的分析表达。然后通过数值积分确定瞬态部分，并添加到由闭合式公式给出的响应。获得有限和无限梁的结果之间的非常良好的巧合，这进一步利用了分析基础刚度突变变化的影响。

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