The dynamic behaviour of an Euler–Bernoulli beam resting on the fractionally damped viscoelastic foundation subjected to a moving point load is investigated. The fractional-order derivative-based Kelvin–Voigt model describes the rheological properties of the viscoelastic foundation. The Riemann–Liouville fractional derivative model is applied for a fractional derivative order. The modal superposition method and Triangular strip matrix approach are applied to solve the fractional differential equation of motion. The dependence of the modal convergence on the system parameters is studied. The influences of (a) the fractional order of derivative, (b) the speed of the moving point load and (c) the foundation parameters on the dynamic response of the system are studied and conclusions are drawn. The damping of the beam-foundation system increases with increasing the order of derivative, leading to a decrease in the dynamic amplification factor. The results are compared with those using the classical integer-order derivative-based foundation model. The classical foundation model over-predicts the damping and under-predicts the dynamic deflections and stresses. The results of the classical (integer-order) foundation model are verified with literature.

中文翻译：

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分阻尼粘弹性基础上欧拉-伯努利梁在移动点荷载作用下的动力响应

研究了位于部分阻尼粘弹性基础上的欧拉-伯努利梁在移动点载荷作用下的动态行为。基于分数阶导数的 Kelvin-Voigt 模型描述了粘弹性基础的流变特性。Riemann-Liouville 分数阶导数模型适用于分数阶导数。应用模态叠加法和三角带矩阵法求解运动的分数阶微分方程。研究了模态收敛对系统参数的依赖性。研究了(a)导数分数阶、(b)动点载荷速度和(c)基础参数对系统动态响应的影响并得出了结论。梁基础系统的阻尼随着导数阶数的增加而增加，导致动态放大系数减小。将结果与使用经典整数阶导数基础模型的结果进行比较。经典基础模型高估了阻尼，低估了动态挠度和应力。经典（整数阶）基础模型的结果已通过文献验证。