摘要
为了研究力学与电子系统中典型强非线性系统的性质,提出求解强非线性刚度的杜芬 范德波振子谐和激励下响应的平均法.基于系统的哈密顿作用量及相位差是慢变量而角变量是快变量原理,通过对角变量的平均推导出系统共振时作用量及相位差的平均方程,给出不同参数时系统稳态响应的频响曲线,经过数字模拟研究了系统锁相运动的稳定性,得到了确定稳定域的近似公式并讨论了该近似公式的适用范围.数值仿真结果表明, 用该平均法预测系统的稳态响应具有很高的精度,且该方法可适用于非常强的非线性系统.
To study the property of typical strongly nonlinear oscillators in mechanical and electronic systems, an averaging method to solve the approximate stationary response of a Duffing-van der Pol oscillator with strongly nonlinear stiffness and weak nonlinear damping subject to harmonic excitation was proposed. The differential equations for Hamiltonian, angle variable and phase were derived, and the property that the Hamilton and phase varied slowly while the angle variable varied rapidly was pointed out. Averaging with respect to angle variable yield the averaged equations for Hamilton and phase, the steady-state amplitude responses of the system were obtained and the stability of the analytical results was discussed. The simulation results show that the proposed averaging method agrees well with those from digital simulation of original system, and can be applied for the system with very strong nonlinearity with high precision.
出处
《浙江大学学报（工学版）》
EI
CAS
CSCD
北大核心
2005年第3期445-448,共4页
Journal of Zhejiang University：Engineering Science
基金
国家自然科学基金资助项目(10002015)
浙江省自然科学基金资助项目(102040).
关键词
杜芬-范德波振子
强非线性系统
哈密顿系统
平均法
Computer simulation
Differential equations
Equations of motion
Frequency response
Hamiltonians
Nonlinear systems
Numerical analysis
