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Method for Determining a Research Model of Nonlinear Two Degree of Freedom Dynamic System

机译：确定非线性两度自由度动态系统研究模型的方法

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This paper presents method for determining mathematical model of a nonlinear two-degree-of-freedom dynamic system. It has been found that the mathematical model of a nonlinear dynamic system with two degrees of freedom can be described by 9 second-order linear differential equations, which are obtained in some way by combining subsystem differential equations based on resonant and parametric frequency. However, it is emphasized that in order to create a proper dynamic mathematical model of a system, it is necessary, in addition to proper determination of its parameters, excitation forces and parametric vibration frequencies, to evaluate also the constraints assigned to this system. The dependence of the magnitude of the amplitudes of the parametric excitation forces on the change of its frequency was determined and the relationship between their number and the nonlinearity of the dynamic system was explained. Methods of creating excitation force matrices and their properties are analyzed as well. It was found that the number of columns of the excitation force matrix, i.e. the length of the rows, depends on the degree of nonlinearity of the dynamic system. The certainty of the analytical methods presented in the paper was verified by numerical calculations.
机译：本文介绍了确定非线性二维自由度动态系统的数学模型的方法。已经发现，通过基于谐振和参数频率组合子系统差分方程，以某种方式获得了具有两度自由度的非线性动态系统的数学模型，其通过组合基于谐振和参数频率的子系统微分方程获得。然而，强调，为了创建一个系统的适当动态数学模型，除了正确确定其参数，激励力和参数振动频率之外，还需要评估分配给该系统的约束。确定参数激励力的幅度的幅度确定在其频率的变化上，并解释了它们的数量与动态系统的非线性之间的关系。分析了创建激发力矩阵的方法及其性质。发现激发力矩阵的列数，即行的长度取决于动态系统的非线性程度。通过数值计算验证了本文中提出的分析方法的确定性。

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