Abstract

The problem of the low-velocity normal impact of a rigid sphere with an infinite viscoelastic Kirchhoff–Love plate is considered. The dynamic behavior of a viscoelastic plate is described by a fractional-derivative standard linear solid model. The fractional parameter, which determines the order of the fractional derivative, takes into account the change in the viscosity of the plate material in the contact zone during impact. The plate buckling and the contact force are determined by the generalized Hertz theory. Using the algebra of Rabotnov operators and considering the effect of bulk and shear relaxation, we obtain an integral equation for the buckling of contacting bodies. An approximate solution of this equation makes it possible to find the time dependence not only for the contact buckling but also for the contact force.

中文翻译：

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考虑体积和剪切松弛的具有无限 Kirchhoff-Love 板的刚性球体的影响

摘要

考虑了具有无限粘弹性 Kirchhoff-Love 板的刚性球体的低速法向碰撞问题。粘弹性板的动态行为由分数阶导数标准线性实体模型描述。决定分数阶导数阶数的分数阶参数考虑了冲击过程中接触区板材粘度的变化。板屈曲和接触力由广义赫兹理论确定。使用 Rabotnov 算子的代数并考虑体积和剪切松弛的影响，我们获得了接触体屈曲的积分方程。该方程式的近似解不仅可以找到接触屈曲的时间依赖性，还可以找到接触力的时间依赖性。