双弹簧振子非线性振动的理论研究  

Theoretical investigation on the nonlinear vibration of two-spring-oscillator system

作　　者：石玉仁[1] 张娟[1] 王彩云[1] 耿碧玉[1] 南伟伟[1] 刘娟[1] 

机构地区：[1]西北师范大学物理与电子工程学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2010年第5期28-33,共6页Journal of Northwest Normal University(Natural Science)

基　　金：教育部科学技术研究重点项目(209128);西北师范大学科技创新工程资助项目(NWNU-KJCXGC-03-53);西北师范大学大学生科技创新项目资助课题

摘　　要：建立了一般情况下双弹簧振子振动的运动微分方程,该方程为一非线性方程组,表明此时振子的运动会出现复杂的结构特征.理论分析表明,在小振幅振动的情形下,当系统纵向振动频率和横向振动频率之比为2时,自由振动的双弹簧振子系统存在内共振现象,数值结果证实了这一结论.The motion equation for the system of two-spring-oscillation is established in the most general case.The equation is a set of nonlinear differential equations,which shows that there exist complex structures in this nonlinear system.Theoretical analysis shows,in the case of small amplitude,that there exist internal resonance phenomena when the frequency vibrating in horizontal direction is 2 times of the frequency vibrating in vertical direction,which is confirmed by the numerical results.

关 键 词：双弹簧振子 非线性振动 内共振 

分 类 号：O322[理学—一般力学与力学基础]