车桥耦合振动迭代求解数值稳定性问题

本文首先建立简化的等效弹簧振子模型进行车桥耦合振动迭代求解稳定性理论分析,然后将分析结论推广到复杂车桥系统进行验证.论文揭示了迭代不收敛的机理,再现了分离迭代发散的现象,提出了解决或者改善迭代稳定性的方法.研究表明迭代计算稳定性主要由所采用的轮轨接触假设决定,轮轨密贴接触假设是迭代不收敛的主要根源,而采用轮轨非密贴接触假设基本不会导致迭代不收敛.若采用轮轨密贴接触假设,在足够小的积分步长下,轮对质量与轮轨接触处桥梁单元的节点集中质量之比是影响迭代稳定性的关键因素,而桥梁和车辆系统的刚度、阻尼是影响迭代稳定性的次要因素.可采取如下方法改善迭代稳定性:忽略轮对惯性力对桥梁的作用,采用迭代加速技术,选用较大的时间积分步长等.

Numerical Stability of Iteration Scheme for Solution of Vehicle-Bridge Coupling Vibration

The charactertics of iteration scheme for the solution of vehicle-bridge coupling vibration were studied.Some simplified Abstract models were established for the theoretical analysis of iterative stability,then the research production was generalized to the vehicle-bridge dynamic system.The mechanics of numerical divergence is disclosed,the phenomenon of divergence reappears and the methods that could solve the divergence problem or enhance numerical stability were presented.The study shows that the numerical stability is mainly determined by the wheel-rail non-closing contact hypotheses.The wheel-rail closing contact hypotheses is the root of divergence problem,while wheel-rail non-closing contact hypotheses is the ultimate method to solve divergence problem.If wheel-rail closing contact hypotheses is adopted,the primary element that influences numerical stability is the ratio of wheelset mass to lumped mass of corresponding bridge node,while the stiffness and damper charactertics of vehicle and bridge is secondary.These method could be used to enhance numerical stability:neglecting wheelset inertia force acting on bridge,applying iteraion accelerating method and employing larger time step and so on.