基于弹性基础的多级并联调谐质量阻尼器设计

Design of Multi-grade Parallel Dynamic Vibration Absorbers on an Elastic Foundation

基于结构弹性基础假设,建立多级并联调谐质量阻尼器数学模型,获取弹性基础阻抗特性,推导主系统振幅无量纲表达式。研究发现地基弹性振动对主系统的影响不可忽略,结合多级并联调谐质量阻尼器对振动衰减的优势,提出对考虑弹性地基的多级并联系统进行优化设计的必要性。分析梁的连接位置距端部长度u对主系统影响规律:u值越小,梁的弹性振动对主系统的影响程度就越小;当u≤1 m,梁第1阶固有频率与主系统第1阶固有频率不发生耦合振动,中间位置(u=2 m时)影响最大。并对此情况下2级并联和4级并联系统参数进行优化设计,优化结果表明:不考虑弹性地基的多级并联系统优化结果对于弹性地基下多级并联系统不再适用,考虑梁的弹性结合数值优化法对多级并联系统进行优化能很好削弱梁的弹性振动对主系统的影响。最后研究连接点动刚度对主系统的影响:当连接点动刚度K≥40kd时,梁第1阶固有频率对主系统前三阶固有频率影响较小;当K≥70 kd时,可忽略弹性梁对调谐质量阻尼器设计的影响。

The mathematical model of the multi-grade parallel dynamic vibration absorber on an elastic foundation was established. The dimensionless expression of the amplitude magnification factor and the impedance of the elastic foundation were gained. It was found that the influence of the elastic foundation on the main system cannot be ignored. Considering its advantage of vibration decay, the necessity to optimize the multi-grade parallel system was proposed. The influence of the distance u between the connection and the end of the beam on the main system was analyzed. It was found that the less u will lead to the smaller influence of the beam elastic vibration on the main system. The first frequency vibration of the beam will not couple with the first frequency vibration of the main system when u≤1 m, and the u has the largest influence on the main system when u=2 m. The numerical optimization method was used to design the parameters of 2-grade parallel and 4-grade parallel systems. The result shows that the result of the rigid connection system is not applicable to the elastic system. The elastic connection system can effectively optimize the multi-grade parallel system and reduce the influence of the beam’s elastic vibration on the main system. Finally, influence of the dynamic stiffness of the connection on the main system was studied. It shows that the first natural frequency of the beam has no effect on the first three nature frequencies when K≥40 kd, and the influence of the beam on the main system can be neglected whenK≥70 kd.