To arrive at an equivalent linear differential equation, the non-perturbative approach (NPA) is established. The corresponding linear equation is employed for performing the structural analysis. A numerical computation demonstrates a high consistency with the precise frequency. The correlation with the numerical solution explains the reasonableness of the obtained solutions. For additional nonlinear kinds of oscillation, the methodology gives an exact simulation. The stable construction of the prototype is shown in a series of diagrams. Positive position feedback (PPF), integral resonant control (IRC), nonlinear integral positive position feedback (NIPPF), and negative derivative feedback (NDF) are proposed to get rid of the damaging vibration in the system. It is found that the NDF control is more efficient than other controllers for vibration suppression. The theoretical methodology is applied by using the averaging method for getting a perturbed solution. The stability and influence of various parameters of the structure are established at main and 1:1 internal resonance, which is presented as one of the worst resonance cases. Association concerning mathematical solution and computational simulation is achieved.

为了得到等效的线性微分方程，建立了非微扰方法（NPA）。采用相应的线性方程进行结构分析。数值计算表明与精确频率具有高度一致性。与数值解的相关性说明了所得解的合理性。对于其他非线性振荡类型，该方法给出了精确的模拟。一系列图表显示了原型的稳定结构。提出了正位置反馈（PPF）、积分谐振控制（IRC）、非线性积分正位置反馈（NIPPF）和负微分反馈（NDF）来消除系统中的破坏性振动。结果发现，NDF 控制比其他控制器更有效地抑制振动。通过使用平均方法来应用理论方法来获得扰动解。在主谐振和 1:1 内部谐振（作为最差谐振情况之一）下建立了结构的稳定性和各种参数的影响。实现了数学求解和计算模拟的关联。