非线性振荡的Volterra级数分析法

Analysis Method of Nonlinear Oscillation Via Volterra Series

在 Volterra级数和非线性转移函数理论的基础上 ,介绍了一种递推算法 ,可以在任意精度内由两个非线性代数方程 (由决定方程产生 )求得非线性振荡器的近似正弦波的幅值与频率 .该法既保留了谐波平衡分析法、描述函数法和平均法的许多期望的特性 ,而且在技巧上与经典的Krylov,Bogoliubov及 Mitropisky等方法有类似之处 ,但比它们简便 .与常规方法不同之处还在于本法对系统的非线性度和振荡的幅值无严格要求 ,而且其求解精度由算法结构所决定 .

Using a novel approach,the amplitude and frequency of nearly sinusoidal nonlinear oscillators can be calculated by solving two algebraic nonlinear equations.These determining equations can be generated to within any desired accuracy using a recursive algorithm based on Volterra series and nonlinear transfer functions. Our method inherits many desirable features of harmonic balance method,the describing function method and averaging method.Our technique is analogous to,but is much simpler than,the classic approach due to Krylov,Bogoliubov,and Mitropoisky.Unlike conventional techniques,however,our appoach imposes no severe restriction in either the degree of nonlinearity,or the amplitude of ossillation.Moreover,the accuracy of the solution is determined by construction of algorithm.