基于PIM法车桥耦合模型Duhamel项迭代格式选择
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U441.3; TH.3

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(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)


Selection of Duhamel Term′s Iterative Algorithm for Vehicle Bridge Coupling Vibration Model Based on Precise Intergration Method
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    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:

    A vehicle-bridge coupling vibration model of a moving spring mass system has been constructed based on mode superposition. Based on Duhamel term′s precise integration method (PIM), Cotes and Gauss algorithms are introduced to solve the nonhomogeneous linear differential equation following the load in an integration step be regarded as coordinating load and constant load. Taking a spring mass system running on simple supported beam as an example, the effects of equivalent nodal load and numerical algorithms for nonlinear differential equation based on Duhamel term are analyzed. The results indicated that the result of Cotes with coordinate load is closer to analytical solution. The way of equivalent load has weak effect on Newmark-β numerical result in vehicle-bridge coupled vibration response. But the results also show that the response curve of vehicle bridge coupling vibration disperse when the equation is solved using Gauss numerical method with coordinate load, and undermined coefficient method has overlarge error at the same time. Research results show that Newmark-β method can meet the engineering accuracy. In order to get the same accuracy as PIM-C-H, Newmark-β method need smaller time integral step and cost more time accordingly in solving the same problem.

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  • 在线发布日期: 2017-11-09
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