基于切比雪夫拟谱法的移动荷载作用下简支梁动力响应计算  

Dynamic response of simply supported beams under moving loads based on Chebyshev pseudo-spectral method

作　　者：向华伟 曾滨[1] 荣华[1,2] 范兴朗 耿岩 XIANG Hua-wei;ZENG Bin;RONG Hua;FAN Xing-lang;GENG Yan(Central Research Institute of Building and Construction Co.,Ltd.,MCC Group,Beijing 100088,China;Inspection and Certification Co.,Ltd.,MCC,Beijing 100088,China)

机构地区：[1]中冶建筑研究总院有限公司,北京100088 [2]中冶检测认证有限公司,北京100088

出　　处：《计算力学学报》2024年第5期903-908,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金面上项目(52078509);国家自然科学基金青年基金项目(52008413);中国博士后科学基金(2023M734085)资助项目。

摘　　要：采用切比雪夫拟谱法求解移动荷载作用下简支梁的动力响应问题,该方法通过重新选取插值点的方式并借助转换矩阵对边界条件进行施加,对集中荷载采用高斯函数法进行正则化处理。将本文方法计算结果与解析解和有限元解进行比较,结果表明,在划分较少单元数量时,采用本文方法计算结果与解析解吻合良好,求解效率高于有限元方法。采用本文方法对Dirac函数的正则化参数σ_(n)进行敏感性分析,结果表明,当在±3σ_(n)范围内布置配点数6~10个时,计算结果能取得较好的精度。The dynamic response of a simply supported beam under a moving load is determined by using the Chebyshev pseudo-spectral method.The boundary conditions of the simply supported beam are imposed by reselecting the interpolation points and using a transform matrix.The concentrated load is regulated by a Gauss function.The computational results from the proposed method are compared with the analytical solutions and the finite element method.The results show that the proposed method with fewer elements is in good agreement with the analytical solution,and displays a higher computational efficiency than the finite element method.In addition,a sensitivity analysis is conducted for the regularisation parameterσ_(n) of the Dirac function.The analysis results indicate that when six to ten collocation points within the range of±3σ_(n) are used,the computational results can achieve high accuracy.

关 键 词：移动荷载 简支梁 动力响应 拟谱法 正则化 

分 类 号：O302[理学—力学]