This paper presents a Dynamic Partitioning Method (DPM) to solve the vehicle-bridge interaction (VBI) problem via a set of exclusively second-order ordinary differential equations (ODEs). The partitioning of the coupled VBI problem follows a localized Lagrange multipliers approach that introduces auxiliary contact bodies between the vehicle’s wheels and the sustaining bridge. The introduction of contact bodies, instead of merely static points, allows the assignment of proper mass, damping and stiffness properties to the involved constrains. These properties are estimated in a systematic manner, based on a consistent application of Newton’s law of motion to mechanical systems subjected to bilateral constraints. In turn, this leads to a dynamic representation of motion constraints and associated Lagrange multipliers. Subsequently, both equations of motion and constraint equations yield a set of ODEs. This ODE formulation avoids constraint drifts and instabilities associated with differential–algebraic equations, typically adopted to solve constrained mechanical problems. Numerical applications show that, when combined with appropriate numerical analysis schemes, DPM can considerably decrease the computational cost of the analysis, especially for large vehicle-bridge systems. Thus, compared to existing methods to treat VBI, DPM is both accurate and cost-efficient.

本文提出了一种动态划分方法（DPM），通过一组专有的二阶常微分方程（ODE）解决了车桥相互作用（VBI）问题。耦合的VBI问题的划分遵循局部拉格朗日乘数法，该方法将辅助接触体引入到车轮和支撑桥之间。接触体的引入，而不仅仅是静态点，允许为涉及的约束分配适当的质量，阻尼和刚度属性。根据牛顿运动定律在受到双边约束的机械系统上的一致应用，可以系统地估算这些属性。反过来，这导致运动约束和相关的拉格朗日乘数的动态表示。随后，运动方程和约束方程都产生一组ODE。这种ODE公式避免了通常用于解决受约束机械问题的微分-代数方程相关的约束漂移和不稳定性。数值应用表明，当与适当的数值分析方案结合使用时，DPM可以大大降低分析的计算成本，尤其是对于大型车桥系统而言。因此，与现有的治疗VBI的方法相比，DPM既准确又具有成本效益。当与适当的数值分析方案结合使用时，DPM可以大大降低分析的计算成本，尤其是对于大型车桥系统而言。因此，与现有的治疗VBI的方法相比，DPM既准确又具有成本效益。当与适当的数值分析方案结合使用时，DPM可以大大降低分析的计算成本，尤其是对于大型车桥系统而言。因此，与现有的治疗VBI的方法相比，DPM既准确又具有成本效益。