LI Yan-ting, XU Ji-qing, XU Xi-bin, PU Yan-ru. A Numerical Method for Calculation of Structural Jerk Responses[J]. Applied Mathematics and Mechanics, 2017, 38(8): 922-931. doi: 10.21656/1000-0887.370181
Citation: LI Yan-ting, XU Ji-qing, XU Xi-bin, PU Yan-ru. A Numerical Method for Calculation of Structural Jerk Responses[J]. Applied Mathematics and Mechanics, 2017, 38(8): 922-931. doi: 10.21656/1000-0887.370181

A Numerical Method for Calculation of Structural Jerk Responses

doi: 10.21656/1000-0887.370181
  • Received Date: 2016-06-06
  • Rev Recd Date: 2017-03-01
  • Publish Date: 2017-08-15
  • Jerk is of great significance in engineering practice. A numerical method for solving jerk responses was constructed through combination of the radial basis function (RBF) approximation and the collocation method. The proposed method was used to calculate the jerk and the 3rd-order jerk equations, and the RBF interpolation was adopted to approximate the real motion rule, which made good the defect that the traditional methods can’t be used to calculate the jerk. Aimed at the numerical characteristics of the dynamic differential equations, an improved RBF expression of multivariable joint interpolation combining the all-order derivatives of the variable was presented. The initial-value condition of the same order with the differential equation was added to obviously decrease the numerical oscillation. The results of the numerical examples indicate that the proposed method has the advantages of a simple calculation process, high accuracy and high applicability to jerk equations.
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  • [1]
    谈开孚, 赵永凯, 郭小弟. 谈加加速度[J]. 力学与实践, 1988,10(5): 46-51.(TAN Kai-fu, ZHAO Yong-kai, GUO Xiao-di. Sduty on jerk[J]. Mechanics in Engineering,1988,10(5): 46-51.(in Chinese))
    梅凤翔, 刘瑞, 罗勇. 高等分析力学[M]. 北京: 北京理工大学出版社, 1991: 251.(MEI Feng-xiang, LIU Rui, LUO Yong. Advanced Analytical Mechanics [M]. Beijing: Beijing Institute of Technology Press, 1991: 251.(in Chinese))
    黄沛天, 黄文, 胡利云. 关于变加速动力学及其应用[J]. 力学与实践, 2004, 26(1): 67-68.(HUANG Pei-tian, HUANG Wen, HU Li-yun. On non-uniformly accelerating dynamics and its application[J]. Mechanics in Engineering,2004, 26(1): 67-68.(in Chinese))
    Chase J G, Barroso L R, Hunt S. Quadratic jerk regulation and the seismic control of civil structures[J]. Earthquake Engineering and Structural Dynamics,2003,32(13): 2047-2062.
    杨学山, 齐霄斋, 李兆治, 等. 基于测量加速度微分量的传感器[J]. 震动与冲击, 2008,27(12): 143-147.(YANG Xue-shan, QI Xiao-zhai, Lee G C, et al. Sensor for measuring the derivative of acceleration component[J]. Journal of Vibration and Shock,2008,27(12): 143-147.(in Chinese))
    何浩祥, 闫维明, 陈彦江. 地震动加加速度反应谱的概念及特性研究[J]. 工程力学, 2011,28(11): 124-129.(HE Hao-xiang, YAN Wei-ming, CHEN Yan-jiang. Study on concept and characteristics of seismic jerk response spectra[J]. Engineering Mechanics,2011,28(11): 124-129.(in Chinese))
    AN Yong-hui, Hongki J, Jr Spencer B F, et al. A damage localization method based on the ‘jerk energy’[J]. Smart Materials and Structures,2014,23(2): 025020. doi: 10.1088/0964-1726/23/2/025020.
    Bertero R D, Bertero V V. Performance-based seismic engineering: the need for a reliable conceptual comprehensive approach[J]. Earthquake Engineering & Structural Dynamics,2002,31(3): 627-652.
    HE Zheng, XU Yi-chao. Correlation between global damage and local damage of RC frame structures under strong earthquakes[J]. Structural Control and Healthy Monitoring,2017,24(3): e1877. doi: 10.1002/stc.1877.
    钟万勰. 结构动力方程的精细时程积分法[J]. 大连理工大学学报, 1994,32(2): 131-136.(ZHONG Wan-xie. On precise time-integration method for structural dynamics[J]. Journal of Danlian University of Technology,1994,32(2): 131-136.(in Chinese))
    胡海岩. 应用非线性动力学[M]. 北京: 航空工业出版社, 2000.(HU Hai-yan. Applied Nonlinear Transient Dynamical [M]. Beijing: Aviation Industry Press, 2000.(in Chinese))
    吴宗敏. 径向基函数、散乱数据拟合与无网格偏微分方程数值解[J]. 工程数学学报, 2002,19(2): 1-12.(WU Zong-min. Radial basis function scattered data interprolation and the meshless method of numerical solution of PDEs[J]. Journal of Engineering Mathematics,2002,19(2): 1-12.(in Chinese))
    陈文, 傅卓佳, 魏星. 科学与工程计算中的径向基函数方法[M]. 北京: 科学出版社, 2014.(CHEN Wen, FU Zhuo-jia, WEI Xing. The Radial Basis Function Methods in Science and Engineering Mathematics [M]. Beijing: Science Press, 2014.(in Chinese))
    WU Zong-min. Compactly supported positive definite radial functions[J]. Advances in Computational Mathematics,1995,4(1): 283-292.
    Wendland H. Piecewise polynomial, positive definite and compactly supported Radial functions of minimal degree[J]. Advances in Computational Mathematics,1995,4(1): 389-396.
    Buhmann M D. Radial functions on compact support[J]. Proceedings of the Edinburgh Mathematical Society,1998,41(1): 33-46.
    徐绩青, 李正良, 吴林键. 基于径向基函数逼近的结构动力响应计算方法[J]. 应用数学和力学, 2014,35(5): 533-541.(XU Ji-qing, LI Zheng-liang, WU Lin-jian. A calculation method for structural dynamic responses based on the approximation theory of radial basis function[J]. Applied Mathematics and Mechanics,2014,35(5): 533-541.(in Chinese))
    李岩汀, 许锡宾, 周世良, 等. 基于径向基函数逼近的非线性动力系统数值求解[J]. 应用数学和力学, 2016,37(3):311-318.(LI Yan-ting, XU Xi-bin, ZHOU Shi-liang, et al. A numerical approximation method for nonlinear dynamic systems based on radial basis functions[J]. Applied Mathematics and Mechanics,2016,37(3): 311-318.(in Chinese))
    汪梦甫, 周锡元. 结构动力方程的更新精细积分方法[J]. 力学学报, 2004,36(2): 191-195.(WANG Meng-fu, ZHOU Xi-yuan. Renewal precise time step integration method of structural dynamic analysis[J]. Acta Mechanica Sinica,2004,36(2): 191-195.(in Chinese))
    张继峰, 邓子辰, 张凯. 结构动力方程求解的改进精细Runge-Kutta方法[J]. 应用数学和力学, 2015,36(4): 378-385.(ZHANG Ji-feng, DENG Zi-chen, ZHANG Kai. An improved precise Runge-Kutta method for structural dynamic equations[J]. Applied Mathematics and Mechanics,2015,36(4): 378-385.(in Chinese))
    Gottlieb H P W. Harmonic balance approach to periodic solutions of nonlinear jerk equations[J]. Journal of Sound and Vibration,2004,271(3/5): 671-683.
    Wu B S, Lim C W, Sun W P. Improved harmonic balance approach to periodic solutions of non-linear jerk equations[J]. Physics Letters A,2006,354(1/2): 95-100.
    Ramos J I. Analytical and approximate solutions to autonomous, nonlinear, third-order ordinary differential equations[J]. Nonlinear Analysis: Real World Applications,2010,11(3): 1613-1626.
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