分类： 交通运输工程 >> 铁路运输 提交时间： 2024-07-26
摘要： In mechanics, common energy principles are based on fixed boundary conditions. However, in bridge engineering structures, it is usually necessary to adjust the boundary conditions to make the structure’s internal force reasonable and save materials. However, there is currently little theoretical research in this area. To solve this problem, this paper proposes the principle of minimum virtual work for movable boundaries in mechanics through theoretical derivation such as variation method and tensor analysis. It reveals that the exact solution of the mechanical system minimizes the total virtual work of the system among all possible displacements, and the conclusion that the principle of minimum potential energy is a special case of this principle is obtained. At the same time, proposed virtual work boundaries and control conditions, which added to the fundamental equations of mechanics. The general formula of multidimensional variation method for movable boundaries is also proposed, which can be used to easily derive the basic control equations of the mechanical system. The incremental method is used to prove the theory of minimum value in multidimensional space, which extends the Pontryagin’s minimum value principle. Multiple bridge examples were listed to demonstrate the extensive practical value of the theory presented in this article. The theory proposed in this article enriches the energy principle and variation method, establishes fundamental equations of mechanics for the structural optimization of movable boundary, and provides a path for active control of mechanical structures, which has important theoretical and engineering practical significance.
分类： 交通运输工程 >> 铁路运输 提交时间： 2024-02-07 合作期刊: 《应用力学学报》
摘要： 针对适于山地轨道交通的齿轨铁路,建立基于显式时间积分的三维齿轨轮对-轨道瞬态接触有限元模型,模型可分析齿轮齿条啮合和轮轨滚动接触间中、高频耦合动力作用。轮对和轨道真实几何,齿轮与车轮轮径差导致“车轮悖论”现象及结构振动等均有考虑,齿轮齿条啮合和轮轨接触采用集成库仑摩擦的“面-面”接触算法求解。对比零和非零轮轨摩擦系数工况,解构“车轮悖论”现象对动态接触的影响。以初步设计的Strub型齿轨铁路为例,分析速度为10 km/h和0‰、240‰、480‰坡度下动态接触现象。结果表明,受齿轮啮合影响,齿条、轮轨接触力均呈现周期性波动,但垂向接触总力和总牵引扭矩分别在重力载荷与牵引扭矩附近波动。“车轮悖论”使齿条垂向力和法向接触应力减小,而轮轨垂向力和法向接触应力增加,齿面切向接触应力与接触斑内滑移区面积相应增加,在坡度240‰下,轮轨摩擦系数由0增至0.2,齿条、轮轨最大法向接触应力由248.69、752.66 MPa增至195.17、757.44 MPa,最大切向接触应力相应由24.48、152.84 MPa变成21.31、2.14 MPa。轮轨接触斑因发生显著蠕滑呈现全滑移。相同速度及摩擦条件下,坡度增加使齿条垂向力和牵引力增加,轮轨垂向力和牵引力减小,接触应力呈同相变化。
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