Significant number of procedures for solving of the finite degree-of-freedom forced nonlinear oscillator are developed. For all of them it is common that they are based on the exact solution of the corresponding linear oscillator. For technical reasons, the aim of this paper is to develop a simpler solving procedure. The rotating vector method, developed for the linear oscillator, is adopted for solving of the nonlinear finite degree-of-freedom oscillator. The solution is assumed in the form of trigonometric functions. Assuming that the nonlinearity is small all terms of the series expansion of the function higher than the first are omitted. The rotating vectors for each mass are presented in the complex plane. In the paper, the suggested rotating vector procedure is applied for solving of a three-degree-of-freedom periodically excited oscillator. The influence of the nonlinear stiffness of the flexible elastic beam, excited with a periodical force, on the resonant properties of the system in whole is investigated. It is obtained that the influence of nonlinearity on the amplitude and phase of vibration is more significant for smaller values of the excitation frequency than for higher ones.

开发了大量用于求解有限自由度受迫非线性振荡器的程序。对于所有这些，它们通常基于相应线性振荡器的精确解。由于技术原因，本文的目的是开发一个更简单的求解过程。采用为线性振子开发的旋转矢量法求解非线性有限自由度振子。该解以三角函数的形式被假定。假设非线性很小，函数级数展开中高于第一项的所有项都被忽略。每个质量的旋转矢量显示在复平面中。在本文中，建议的旋转矢量程序用于求解三自由度周期激励振荡器。研究了用周期性力激发的柔性弹性梁的非线性刚度对整个系统谐振特性的影响。结果表明，非线性对振动振幅和相位的影响对于较小的激励频率值比对于较高的激励频率值更显着。