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A lattice model for transition zones in ballasted railway tracks
Journal of Sound and Vibration ( IF 4.7 ) Pub Date : 2021-03-01 , DOI: 10.1016/j.jsv.2020.115840
João Manuel de Oliveira Barbosa , Andrei B. Fărăgău , Karel N. van Dalen

Abstract The procedure presented in this work aims at providing a framework for studying settlement of ballast in zones with stiffness variation of the railway track support. The proposed procedure results from expanding an existing infinite periodic model of a railway track to account for variations in the stiffness of the foundation. Ballast is simulated via a linear lattice, whose dynamic response differs from that of a continuum. The expanded model is composed of three regions: a left region, which is semi-infinite and periodic; a mid-region, of finite length and where the properties of the foundation can change; and a right region, which is also semi-infinite and periodic and whose properties can differ from those of the left region. The equations of motion of the mid-region are written directly in the time domain, with the rail being described by finite elements. On the other hand, the left and right semi-infinite regions are treated semi-analytically in the frequency domain, and afterwards their responses are converted to the time domain, resulting in convolution integrals prescribed at the boundaries of the mid-region that simulate non-reflective boundaries. The final model only contains the degrees of freedom corresponding to the mid-region (which can be as short as the region where the stiffness variation is present), and that leads to faster calculations than if the boundaries were placed further away to dissipate undesired reflections. The method is cast in the time domain, and all elements are assumed to behave linearly. In the future, the model will be expanded to incorporate non-linear behaviour of the ballast. The presented method is validated by means of simple examples, and afterwards applied to a real scenario in which a culvert crosses a railway track. As presented, the method can be used to study the linear dynamics of transitions zones, study mitigation measures, and infer about indicators like force transmitted and energy dissipated, which might be useful to assess the development of settlement of the ballast.

中文翻译:

有碴轨道过渡区的格子模型

摘要 这项工作中提出的程序旨在为研究铁路轨道支架刚度变化区域中道碴沉降提供一个框架。提议的程序是通过扩展现有的铁路轨道无限周期模型来解决基础刚度的变化。镇流器通过线性点阵进行模拟,其动态响应与连续体不同。扩展模型由三个区域组成:左区域,半无限和周期性;一个中间区域,长度有限,并且基础的属性可以改变;右侧区域也是半无限和周期性的,其性质可能与左侧区域不同。中间区域的运动方程直接写在时域中,轨道由有限元描述。另一方面,左半无限区域和右半无限区域在频域进行半解析处理,然后将它们的响应转换到时域,导致在模拟非的中间区域边界处规定卷积积分。 - 反射边界。最终模型仅包含对应于中间区域的自由度(可以与存在刚度变化的区域一样短),与将边界放置得更远以消散不需要的反射相比,这会导致计算速度更快. 该方法在时域中进行转换,并且所有元素都假定为线性行为。将来,该模型将扩展到包含镇流器的非线性行为。通过简单的例子验证了所提出的方法,然后将其应用于涵洞穿过铁路轨道的实际场景。如上所述,该方法可用于研究过渡带的线性动力学,研究缓解措施,并推断力传递和能量耗散等指标,这可能有助于评估道碴沉降的发展。
更新日期:2021-03-01
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