基于非线性弹簧阻尼模型的球体碰撞模拟
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摘要
基于动态接触模型对碰撞接触过程进行建模和数值计算,分析了模型各参数的物理意义,并与经典力学接触模型进行对比,通过恢复系数与阻尼系数的关系,将两类模型联系起来。使用Roung-Kutta方法求解动力学方程,并将模型结果与ABAQUS显式动力学模拟结果及实验结果进行比较。对比结果表明,非线性阻尼模型能够较为准确地反映碰撞接触过程。研究工作验证了模型及各参数选取的合理性,比较了各模型特点,为接触过程模型选取提供了参考。
Dynamic contact models are applied to simulate the process by numerical computation. Model parameters are analyzed and models are compared with classical mechanics contact model. Two kinds of models are connected by the relationship between coefficient of restitution and damping coefficient. It applies Roung-Kutta method to solve dynamic equations and compare the results with ABAQUS explicit dynamics simulation and experiments. It concludes that nonlinear spring damper model could simulate the contact process with relatively high accuracy. The method and parameters are verified to be correct,which offers reference for choosing contact models.
Dynamic contact models are applied to simulate the process by numerical computation. Model parameters are analyzed and models are compared with classical mechanics contact model. Two kinds of models are connected by the relationship between coefficient of restitution and damping coefficient. It applies Roung-Kutta method to solve dynamic equations and compare the results with ABAQUS explicit dynamics simulation and experiments. It concludes that nonlinear spring damper model could simulate the contact process with relatively high accuracy. The method and parameters are verified to be correct,which offers reference for choosing contact models.
引文
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[2]牛学仁,戴保东.理论力学[M].北京:国防工业出版社,2013.
[3]彼得艾伯哈特,胡斌.现代接触动力学[M].南京:东南大学出版社,2003.
[4]秦志英,陆启韶.基于恢复系数的碰撞过程模型分析[J].动力学与控制学报,2006,4(04):294-298.
[5] R. H. Bao,T. X. Yu. Collision and rebound of ping pong balls on a rigid target[J]. Material and Design,2015,(87):278-286。
[6]王繁生.带式输送机柔性多体动力学分析方法[M].徐州:中国矿业大学出版社,2013.
[7] W. T.汤姆逊.振动理论及其应用[M].胡宗武(译).北京:煤炭工业出版社,1980.
[8] H. M. Lankarani,P. E. Nikravesh. Continuous Contact Force Models for Impact Analysis in Multi-body System[J]. Nonlinear Dynamics,1994,(05):193-207.
[9] X. W. Zhang,Z. Tao,Q. M. Zhang. Dynamic behaviors of visco-elastic thin-walled spherical shells impact onto a rigid plate[J]. Latin American Journal of Solids and Structures,2014,11(14):2607-2623.
[10] D. Karagiozova,X-W Zhang,T-X. Yu. Static and dynamic snapthrough behavior of an elastic spherical shell[J]. Acta Mechanica Sinica,2012,28(03):695-710.
[11] X. W. Zhang,Z. Tao,Q. M. Zhang. Dynamic behavior of visco-elastic thin walled spherical shells impact onto a rigid plate[J]. Latin American Journal of Solids and Structures,2014,(11):2607-2623.
[12]李庆扬.数值分析[M].北京:清华大学出版社,2001.