宽频结构被动非线性消振理论分析及实验验证

The passive nonlinear vibration wide-frequency structure with a nonlinear absorber is studied by applying nonlinear dynamics and nonlinear output frequency response functions, including dense frequency and low stiffness are under consideration in this proposal. The approximate analytical method is developed in order to obtain initial critical condition of the optimal targeted energy transfer for the equivalent dynamic model of the vibration controlling system. Using it as basis, the energy exchange and nonlinear dynamic behaviors of this system are investigated. The dominant analytic expressions of the vibration transmissibility in the dynamics system with nonlinear vibration absorber are established through applying and developing the nonlinear output frequency response functions. The effects of the absorber parameters and the effectiveness of dense frequency, low stiffness are highlighted. The effect of vibration control from the perspective of energy is further evaluated by the index of the transient energy absorptivity. To discuss the vibration control system with nonlinear vibration absorber, the numerical simulation models of nonlinear dynamics are investigated. The accuracy of the theoretical analysis is verified through the corresponding experiments. The results of this research are expected to contribute to the development and improvement of the theories about complex nonlinear dynamics, and provide specific theory references for the design and production for the wide-frequency structure vibration control in the engineering industry.

考虑宽频结构的低刚度等特征，应用非线性动力学和非线性输出频率响应函数理论，研究具有非线性消振器的宽频结构系统被动非线性振动控制机理。通过振动控制系统的等效动力学模型，发展近似解析方法确定最优靶能量传递的初值临界条件，并以此为基础研究系统内的能量变换及其非线性动力学行为；应用和发展非线性输出频率响应函数理论建立含有非线性消振器动力学系统的振动传递率显性解析式，其中重点讨论非线性消振器的参数对系统振动控制效果的影响，并通过瞬态能量吸收率指标从能量角度进一步评价振动控制效果。对具有非线性消振器的振动控制系统，研究非线性动力学的仿真建模方法，进一步讨论振动控制效果；通过非线性消振器的振动控制效果实验，验证理论分析的正确性。研究的成果将会发展和完善复杂非线性动力学与控制理论，并为工程中各种宽频结构的振动控制方案设计提供具体的理论参考。

整星系统具有宽频特性，对其减振能够改善航天器发射过程的动力学环境。本项目提出了一种适用于整星减振的非线性消振器，并对引入了非线性消振器的整星系统的缩比模型进行了振动传递率扫频实验。实验结果表明，该非线性消振器可以在很宽的频率范围内对整星系统进行有效的振动抑制。引入非线性消振器几乎不改变整星系统的固有频率。建立了整星系统的有限元模型，并通过实验结果验证了该有限元模型。利用整星系统的有限元模型，得到了该整星系统的等效两自由度模型，该两自由度模型的两阶固有频率与有限元模型的前两阶固有频率一致。实验模型、有限元模型和等效两自由度模型的结果都表明，通过增加非线性消振器的质量和阻尼，并减小其非线性刚度，可以获得更好的减振效果。通过两自由度模型计算得到的能量吸收率和能量交换结果表明，一个经过合理设计的非线性消振器可以在很宽的频率范围内有效的吸收和耗散能量。