基于PIM法车桥耦合模型Duhamel项迭代格式选择

发布时间：2018-10-24 07:36

【摘要】：考虑荷载在积分步长内的协调分解和不变常量,结合模态综合叠加技术,建立移动弹簧质量车桥耦合振动模型,引入精细积分算法(precise intergration method,简称PIM),并采用科茨及高斯积分格式展开精细积分中Duhamel非齐次项进行求解。以移动弹簧质量车模型作用于简支梁桥为例,分析积分步内荷载等效方法及Duhamel非齐次项展开方式对车桥耦合振动响应的影响。研究结果表明:荷载协调分解并结合科茨积分格式计算结果与解析解更接近,Newmark-β法积分步长内荷载分解形式对计算结果影响较小;荷载协调分解的高斯积分格式计算结果呈发散趋势,待定系数法计算结果与实际偏离较大;Newmark-β法能满足工程需要,但在保证相同计算精度时,需采用较小积分步长、同时耗费较多计算时间;与其他几种数值方法相比,积分步长内荷载协调分解并将科茨积分格式引入精细积分的算法(PIM-Cotes-Harmonize,简称PIM-C-H法),具有快速收敛且计算快的优势。
[Abstract]:Considering the coordinated decomposition of load in integral step and invariant constant, combined with modal synthesis superposition technique, the coupled vibration model of moving spring mass vehicle-bridge is established. In this paper, the precise integration algorithm (precise intergration method,) is introduced for short PIM), and the inhomogeneous terms of Duhamel in precise integration are solved by using Coates' and Gao Si's integral schemes. Taking the moving spring mass vehicle model acting on a simply supported beam bridge as an example, the effect of the integral in-step load equivalent method and the Duhamel inhomogeneous term expansion method on the coupled vibration response of the vehicle and bridge is analyzed. The results show that the results of load coordination decomposition and Coates integral scheme are closer to the analytical solution, and the Newmark- 尾 method has little effect on the calculation results. The result of Gao Si's integral scheme with coordinated load decomposition shows a divergence trend, and the calculation result of undetermined coefficient method deviates greatly from the actual situation. The Newmark- 尾 method can meet the needs of engineering, but the small integral step should be used to ensure the same calculation precision. Compared with other numerical methods, the integral step load is decomposed harmoniously and the Coates integral scheme is introduced into the precise integral algorithm (PIM-Cotes-Harmonize, for short PIM-C-H method), which has the advantage of fast convergence and fast calculation.
【作者单位】：东南大学交通学院;华东交通大学土木建筑学院;
【基金】：国家自然科学基金资助项目(51468018,51268013) 江西省教育厅科研资助项目(GJJ14384) 教育部工程研究中心资助项目(13TM02)
【分类号】：U441.3

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