混频振荡与功率平衡的研究

Research on mixing oscillation and power balance

以三次方变阻尼项和两个不同频激励源混频为例,首先用谐波平衡原理求出微分方程中的三个主谐波解,通过多个计算程序列表验证正确性,同时用频域分析方法与功率平衡理论求出各谐波成份相互之间的非线性耦合关系,证明网络中每一频率成份的复功率各自守恒,两种方法相互印证求解结果。同时用仿真软件输出主谐波解相图,分析得出三个主谐波混频造成的振荡解,其公共基频很低,稳态的总体输出有很长的振荡周期,频谱的分布非常密集,当相点画出的相图还没有完成一个周期时,就显示为非周期性的混沌。

The cube variable damping term and frequency mixing with two different excitation sources are taken as an example in this paper.The harmonic balance principle is used to solve the three main harmonic solutions of differential equation,and their correction is verified with multiple lists of calculation procedure.The frequency domain analysis method and power balance theory are used to solve the nonlinear coupling relationship among various harmonic components to verify that the complex power of each frequency component in networks observes the conservation respectively.The solving results are validated with two method.The phase diagram of main harmonic solution is output by means of simulation software.The oscillation solution generated by frequency mixing of three main harmonic components is analyzed.The analysis results show that the common fundamental frequency is very low,the overall steady output has long oscillation period,and the spectral distribution is intensive.It acts as the nonperiodic chaos when the phase diagram plotted by phase point isn′t completed in a cycle.