摘要
突变理论研究的是一种稳定状态突然转变为另一种稳定状态的现象和规律.以Euler两端铰支压杆为例,考虑载荷作用点的位置及载荷大小的影响,利用弹性系统动力学总势能不变值原理对压杆的力学模型进行受力分析,推导出压杆的势函数方程.将势函数方程与突变理论相结合,画出尖点突变模型,通过分析突变流形图和分叉集可以得到压杆失稳变形的临界条件.结果表明,弹性压杆的承载能力随着载荷作用点偏离压杆中点距离的增加而急剧下降.
Catastrophe theory studies the phenomenon and laws of sudden transition from one stable state to another.Taking Euler's hinged compression bar as an example,considering the influence of the position of the loading point and the magnitude of the load,the mechanical model of the compression bar is analyzed by using the principle of invariant total potential energy of elastic system dynamics,and the potential function equation of the compression bar is deduced.Combining potential function equation with catastrophe theory,a cusp catastrophe model is drawn.By analyzing catastrophe manifold and bifurcation set,the critical condition of buckling deformation of compression bar can be obtained.The results show that the bearing carrying capacity of the elastic compression rod decreases sharply with the increase of the distance of the load acting point diverges from the middle point of the compression bar.
作者
张文静
刘学文
张卜
ZHANG Wen-jing;LIU Xue-wen;ZHANG Bu(School of Mechanical and Auto motive Engineering,Shanghai University of Engineering Science,Shanghai 201620,China)
出处
《数学的实践与认识》
北大核心
2020年第22期208-215,共8页
Mathematics in Practice and Theory
基金
国家自然科学基金项目(51675324)
新能源汽车振动噪声测试与控制专业技术服务平台(18DZ2295900)
上海市地方能力建设(19030501100)。
关键词
尖点突变
屈曲
失稳变形
临界条件
cusp catastrophe
buckling
instability deformation
critical condition
