钢板夹层阻尼高频TMD两阶段设计方法

Two-Step Design Method of High Frequency Sandwich Damping Steel Tuned Mass Damper

随着工业化的发展,建筑结构逐渐轻量化,机械设备逐渐重型化、高效化,这使得机械设备高频扰力导致的结构振动问题越来越突出;为了减轻结构的高频受迫振动响应,可以在结构振动响应较大的位置安装高频高阻尼比的钢板夹层阻尼悬臂梁式调谐质量阻尼器(tuned mass damper,TMD)。由于TMD的弹性元件与阻尼元件相互耦合,因此根据TMD的目标参数进行TMD尺寸设计时需要反复迭代;为了提高设计效率,提出了解耦的TMD两阶段快速设计方法。首先根据模态应变能法推导得到了夹层阻尼悬臂梁的一阶模态阻尼比公式,根据截面弯矩转角关系推导了夹层阻尼悬臂梁的复合截面抗弯刚度公式,进而得到了夹层阻尼悬臂梁结构的动力特性计算公式,公式表明夹层阻尼悬臂梁的动力特性相互耦合。而后,利用推导的公式研究了几何参数对钢板夹层阻尼悬臂梁的一阶频率和模态阻尼比的影响,结果表明结构各部分尺寸的等比例缩放不影响构件的阻尼比,得出了阻尼比与频率可解耦的规律。据此规律提出了高频TMD的两阶段快速设计方法及流程:先根据TMD的目标阻尼比确定结构各部分之间的尺寸关系,然后根据目标频率确定构件尺寸。最后,运用所提出的方法,给出了微型化高频高阻尼比夹层阻尼悬臂梁集合式TMD的设计示例,并对示例模型进行了有限元分析,有限元计算结果与设计目标的偏差小于2%,进一步验证了所提方法的有效性。

With the development of industrialization,building structures tend to be lightweight,and mechanical equipment becomes more and more heavy and efficient.This makes the vibration problem of structures,caused by the disturbance of high-frequency mechanical equipment,more and more prominent.In order to solve the problem,constrained damping structures can be used as a high-frequency-and-high-damping-ratio tuned mass damper(TMD)to control structural vibrations in the position of structures with high vibration.Since the elastic elements and damping elements of TMD are coupled with each other,it is necessary to iteratively design the size of TMD according to the target parameters of TMD.In order to improve the design efficiency,a two-step rapid design method of decoupled TMD is proposed in this paper.Firstly,the first-order modal damping ratio formula of the sandwich damping cantilever beam is derived based on the modal strain energy method,and the composite section bending stiffness formula of the sandwich damping cantilever beam is derived according to the relationship between section moment and rotation angle.Then,the formula of dynamic characteristics of sandwich damping cantilever beam structure is obtained.The formula shows that the dynamic characteristics of sandwich damping cantilever beam are coupled with each other.After that,the influence of geometric parameters on the first-order frequency and modal damping ratio of the cantilever beam is studied using the derived formula.The results show that the damping ratio of each part of the structure has no influence on the damping ratio,meaning the law that the damping ratio and the frequency can be decoupled.A two-step rapid design method and process for high-frequency TMD is then proposed.Firstly,the size relationship between the parts of the structure is determined according to the target damping ratio of TMD,and then the size of components is determined according to the target frequency.Finally,an example of the design of a miniaturized TMD at high frequency and high damping ratio is given.The finite element analysis of the sample model shows that the deviation between the finite element calculation result and the design target is less than 2%,which further verifies the effectiveness of the proposed method.