负刚度吸振器对有限长弹性梁的抑振效果研究

考虑不同形式负刚度动力吸振器对有限长弹性简支梁动态响应的影响，提出并建立"弹性梁-负刚度动力吸振器"耦合系统动力学模型。基于模态叠加法，推导得到各阶模态对应幅频响应解析表达式。以弹性梁第1阶振动模态作为振动抑制目标，结合固定点理论和最大值最小化优化准则得到各类型动力吸振器的最优设计参数。以功率流作为振动控制效果的评价指标，建立"弹性梁-动力吸振器"耦合系统的导纳功率流理论模型。在此基础上，计算得到安装动力吸振器前后弹性梁的总功率流和净功率流，以及动力吸振器消耗的功率流，研究不同形式动力吸振器的振动抑制效果。最后，选择振动控制效果最显著的动力吸振器作为研究对象，针对部分主要设计参数展开研究。计算结果表明：在目标控制模态频率附近，负刚度动力吸振器对弹性梁动态响应的控制效果较好，且多个振动模态响应均被有效控制；当阻尼元件和负刚度元件同时接地对弹性梁动态响应的控制效果最佳；众多设计参数均存在最优值。

A study on vibration suppression effect of a finite elastic beam with a negative stiffness vibration absorber

Considering the influences of different forms of negative stiffness dynamic vibration absorbers on the dynamic responses of a finite elastic simply supported beam, the coupling dynamics models of the elastic beam with a negative stiffness dynamic vibration absorber were proposed. Based on the modal superposition method, the established model was used to derive the analytical expressions of response amplitude corresponding to each mode. Taking the first-order vibration mode of the elastic beam as the vibration suppression target, the optimal design parameters of different types of dynamic vibration absorbers were presented according to the fixed-point theory and the maximum minimization optimization criterion. Taking the power flow as the evaluation index of the vibration control performance, theoretical models of the admittance power flow of the elastic beam with dynamic vibration absorbers were established. Furthermore, the total and net power flows and the power flow consumption of the elastic beam and the dynamic vibration absorber was analyzed, respectively, and the vibration suppression characteristic for different forms of dynamic vibration absorber was studied. Finally, the model with the most significant vibration control performance was selected as the research object, and the parametric studies were carried out by taking some main design parameters into account. The calculation results show that the vibration control effect of the negative stiffness dynamic vibration absorber on the dynamic response of the elastic simply supported beam is significantly better than that of the linear vibration absorber, and multiple vibration modes responses have been suppressed significantly, near the natural frequencies of the controlled modes. When the damping element and the negative stiffness element are grounded at the same time, the control effect on the elastic beam dynamic response is the best. Many design parameters of the negative stiffness dynamic vibration absorber have the optimal values.