Stability of Beam Bridges Under Bridge-Vehicle Interaction

Ayoub El Amrani,Hafid Mataich,and Bouchta El Amrani

车桥耦合状态下梁桥稳定性研究

阿尤布·阿姆拉尼，哈菲德·马泰奇，布赫塔·阿姆拉尼

Abstract: In this paper, we provide an accurate and reliable formulation for simulating the interactions of both train/bridge subsystems and suitable for high-speed railway lines as well as for existing lines worldwide that are being renewed or modernized. We model the train as a series of suspended masses, taking into account the energy dissipation and the suspension system for each train vehicle. On the other hand, the bridge supporting the rails with irregular elevations will be modeled as an Euler-Bernoulli beam. The mathematical formulation of the interaction problem between the two subsystems requires the writing of two sets of equations, which interact with each other through contact forces. Using a one-dimensional finite element formulation, a series of equations are constructed by Modeling the beam structure. In addition, the suspended mass equations are first discretized using Newmark's finite difference formulas, which then reduce the degrees of freedom (DOF) of the vehicle to those of the bridge element. This solves the coupling problem between the two subsystems. The derived component is known as the vehicle/bridge interaction (VBI) element. On the other hand, an iterative procedure will be used subsequently to solve the non-linearity problem of the resulting system of differential equations. MATLAB programs provide results that identify the critical parameters influencing the bridge's dynamic stability.

摘要：在本文中，我们为模拟列车/桥梁子系统的相互作用提供了一种准确可靠的方法，适用于高速铁路线以及世界各地正在更新或现代化的既有铁路线。我们将列车建模为一系列悬浮质量，并考虑了每辆列车的能量耗散和悬挂系统。一方面，支撑不规则高程钢轨的桥梁将被建模为欧拉-伯努利梁。这两个子系统耦合问题的数学公式需要编写两组方程，这两组方程通过接触力相互作用。本研究通过对梁结构建模，使用一维有限元公式构建了一系列方程。另外，本研究首先使用纽马克有限差分公式对悬挂质量方程进行离散化，从而将车辆的自由度 (DOF) 简化为桥梁元素的自由度 (DOF)。这样就解决了两个子系统之间的耦合问题，得出的部分称为车辆/桥梁相互作用（VBI）元素。另一方面，本研究后续将使用迭代程序来解决衍生微分方程系统的非线性问题。MATLAB 程序提供的结果可确定影响桥梁动态稳定性的关键参数。

Key words: Beam bridge; Railway bridge stability; High-speed train; Suspended mobile mass; Bridge-vehicle interaction, beam vibration, iterative procedure; Newmark.

关键词：梁桥；铁路桥稳定性；高铁；悬浮移动质量；车桥耦合，桥梁振动，迭代过程；纽马克

Source: WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS

DOI:10.37394/232011.2024.19.6

Date: May 13, 2024

检索：刘羽茜

翻译：李羿雯

一审：刘羽茜

二审：彭莉

三审：罗玲娟

上传发布：姜浩