摘要
针对原点反共振振动机的力学模型,在考虑了立方非线性弹簧及弹簧静变形等因素后,建立二阶非线性系统动力学控制方程.由此得到系统产生内共振的条件并应用多尺度法建立了平均方程,研究了不同结构参数对系统非线性动力学特性的影响.研究结果表明:当激振力频率小于反共振频率时,非线性的影响可以忽略不计;当大于反共振频率时,非线性的影响增强,振幅出现分叉,并且这种影响随着激振力频率与反共振频率的偏离程度的增大而加强.
In consideration of the cubic nonlinear spring and spring static deformation,the dynamic control equations of second order nonlinear system were established for the mechanical model of driving point anti-resonant vibrating machines.The condition of the system producing internal resonance was obtained and the average equation was established with the multi-scale method.Moreover,the effects of different structural parameters on the nonlinear dynamics characteristics were studied.The results showed that the influence of nonlinear can be ignored when the exciting force frequency is smaller than the anti-resonant one,on the contrary,the influence can be enhanced and the amplitude appear bifurcation which becomes larger with the increasing difference between exciting force and anti-resonant frequency.
出处
《东北大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2012年第5期715-718,共4页
Journal of Northeastern University(Natural Science)
基金
国家自然科学基金资助项目(51105066)
关键词
反共振
内共振
非线性
动力学特性
多尺度
anti-resonance
internal resonance
nonlinear
dynamic characteristics
multi-scale
