The dynamic response of a viscoelastic multilayered pavement under falling weight deflectometer (FWD) loading is an attractive topic for the pavement engineers. Starting from the governing equations, the Laplace transform is first applied to suppress the time variable. The ordinary differential equations (ODE) of the governing equations in Laplace domain are derived by the cylindrical vector functions systems. On the basis of the facts that the top and bottom boundary conditions dual appear, a novel analytical method called dual variable and dual boundary (DVDB) for the ODE is proposed combined with dual variable and position method (DVP). The final solution in time domain is obtained by the inverse Laplace transform that is accelerated by Epsilon algorithm. The solutions of the thin layer issues and imperfect interface conditions are also investigated. Some numerical results from DVDB for the dynamic response of multilayered pavement loaded by FWD discrete pulse series are compared and discussed. It can be concluded that the DVDB combined with Laplace transform can efficiently solve the dynamic response of multilayered pavement in time domain. Furthermore, it can also be suited for some cases, such as material anisotropy properties, thin layers in the structure and interface conditions.

中文翻译：

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FWD加载的多层路面动力响应方法

粘弹性多层路面在落锤式挠度计 (FWD) 载荷下的动态响应对路面工程师来说是一个有吸引力的话题。从控制方程开始，首先应用拉普拉斯变换来抑制时间变量。拉普拉斯域控制方程的常微分方程 (ODE) 是由圆柱向量函数系统导出的。基于上下边界条件对偶出现的事实，结合对偶变量和位置法(DVP)，提出了一种新的常微分方程分析方法，称为对偶变量和对偶边界(DVDB)。通过 Epsilon 算法加速的拉普拉斯逆变换得到时域的最终解。还研究了薄层问题和不完美界面条件的解决方案。比较和讨论了 DVDB 中由 FWD 离散脉冲序列加载的多层路面动态响应的一些数值结果。可以得出结论，DVDB结合拉普拉斯变换可以有效地解决多层路面的时域动力响应问题。此外，它还适用于某些情况，例如材料各向异性属性、结构中的薄层和界面条件。