This work underlines the importance of the application of fractional-order derivative damping model in the modelling of the viscoelastic foundation, by demonstrating the effect of various orders of the fractional derivative on the dynamic response of plates resting on the viscoelastic foundation, subjected to concentrated step load. The foundation of the plate is modelled as a fractionally-damped Kelvin–Voigt model. Modal superposition method and Triangular strip matrix approach are used to solve the partial fractional differential equations of motion. The influence of (a) fractional-order derivative, (b) foundation stiffness, and (c) foundation damping viscosity parameter on the dynamic response of the plate are investigated. Theoretical results show that with the increase in the order of derivative, the damping of the system increases, which leads to decreased dynamic response. The results obtained from the fractional-order damping model and integer-order damping model are compared. The results are verified with literature and numerical results (ANSYS).

中文翻译：

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关于部分阻尼粘弹性地基上板的瞬态响应

这项工作通过演示分数阶导数阻尼模型对搁置在集中台阶下的粘弹性基础上的板的动力响应的影响，强调了分数阶导数阻尼模型在粘弹性基础建模中的重要性。加载。板的基础建模为分数阻尼的Kelvin–Voigt模型。模态叠加法和三角带矩阵法用于求解运动的偏分数阶微分方程。研究了（a）分数阶导数，（b）基础刚度和（c）基础阻尼粘度参数对板动力响应的影响。理论结果表明，随着导数阶数的增加，系统的阻尼增加，导致动态响应降低。比较了从分数阶阻尼模型和整数阶阻尼模型获得的结果。结果得到了文献和数值结果（ANSYS）的验证。