再议秋千参数自激振动的数学模型与数值模拟  

Reconsideration of the mathematic model and numerical simulation of swingwith parametric self-excited oscillation

作　　者：杨百愚[1] 王翠香 王斌科[1] 李春旺 范琦 田昌会[1] YANG Bai-yu;WANG Cui-xiang;WANG Bin-ke;LI Chun-wang;FAN Qi;TIAN Chang-hui(Department of Basic Sciences,Air Force Engineering University,Xi an,Shaanxi,710051,China;Engineering College,Xi an International University,Xi an,Shaanxi,710077,China)

机构地区：[1]空军工程大学基础部,陕西西安710051 [2]西安外事学院工学院,陕西西安710077

出　　处：《大学物理》2020年第10期60-63,共4页College Physics

基　　金：国家自然科学基金项目(51575524)资助。

摘　　要：将秋千视为可变长度单摆,基于高斯函数构造了摆球相对摆杆的速度表达式,式中参数独立于秋千的运动,从而使其在秋千大摆角摆荡时也能符合“高蹲低站”的要求.并以此为基础,建立了秋千的动力学微分方程,进而对秋千运动进行了数值模拟,得到了秋千的运动规律和功能转化的机制.The swing is regarded as a variable length simple pendulum.Based on Gauss function,the velocity of pendulum ball relative to pendulum rod is designed.When the swing moves with a large angle,it can meet the requirements of“squatting down on the highest point and standing up on the lowest point”,because its parameters are independent of swing motion.On this basis,the dynamic differential equation of swing is established,and the motion of swing is simulated numerically,the motion process,work and energy transformation mechanism of swing are obtained.

关 键 词：秋千 参数自激振动 数学模型 数值模拟 

分 类 号：O313.2[理学—一般力学与力学基础]