一类双参数Rayleigh方程的摄动增量解法

Perturbation Incremental Method for a Class of Rayleigh Equations with Two Parameters

运用摄动增量法,研究了一类双参数的Rayleigh方程的极限环.首先运用摄动法,求出λ=0时的极限环的零阶摄动解和参数μ,再运用参数增量法,突破了控制参数必须为小参数的局限,增量过程中运用谐波平衡法解决求解线性方程组问题.然后通过控制参数λ的大小,得到满足一定精确度的极限环的解析表达式.最后通过数值模拟,固定增量大小,将得到的结果与数值积分法得到的结果作比较,表明该方法是有效的.

In this paper,the perturbation incremental method is used to study limit cycles of a class of Rayleigh equations with two parameters.Firstly,the perturbation method is used to obtain the zero order perturbation solution of limit cycle and parameterμwhenλ=0.Then,the parameter incremental method is used to break through the limitation that the control parameters must be small parameters.In the incremental process,the harmonic balance method is used to solve the problem of solving linear equations,the analytical expressions of limit cycles satisfying certain accuracy are obtained by controlling the parameterλ.Finally,through fixed increments and numerical simulation,the results are compared with those obtained by numerical integration method,which show that the method is effective.