基于气体-颗粒两相流理论的颗粒阻尼悬臂梁振动响应预估

Prediction on Vibration Response of Cantilever Particle-damping Beam Based on Two-phase Flow Theory of Gas-particle

在前期工作的基础上,提出一种基于气体-颗粒两相流理论的颗粒阻尼改进模型。该模型将颗粒之间的摩擦效应表述为与碰撞效应一致的等效黏度形式,使得整个模型具有更完整的统一性,方便后续更深入的研究。单自由度(Single degree offreecdom,SDOF)系统的自由振动及强迫振动分析表明该模型相对于原有模型具有更高的预估精度。应用该模型并结合有限元法进行典型颗粒阻尼连续体结构——颗粒阻尼悬臂梁的强迫振动响应预估与分析。结果表明颗粒阻尼是一种较强依赖于结构振动幅值的非线性阻尼,其阻尼效果随着阻尼器的施加位置不同而存在明显的变化。为获得良好的减振效果,尽可能将颗粒阻尼器置于结构振动剧烈的部位。开发的气体-颗粒两相混合流的等效黏性阻尼改进模型对于更为复杂的颗粒阻尼结构的振动与声辐射响应预估奠定了基础。

An improved analytical model using the two-phase flow theory of gas-particle is presented based on previous work, in which the effects due to inter-particle collision and fiiction are all expressed as the equivalent viscosities in a unified way. This makes the entire model has a more complete uniformity and provides convenience for further studies in depth. The analysis results of the free vibration and forced vibration of SDOF systems with particle damping show that the prediction of the improved model is more accuracy than that. of the origin model. Furthermore, the forced response of a typical continuum structure, i.e. the cantilever particle-damping beam is predicted and analyzed using this improved model and the finite element method. Numerical results show that the particle damping is a kind of nonlinear damping, which is highly depended on the vibration amplitude. When the particle damper is exerted on different positions of the beam, the damping properties can present an obvious change. The ideal damping effect can be achieved by putting the particle damper on the position of the structure with high-level vibration. The improved model of equivalent viscous damping based on two-phase flow theory of gas-particle developed can lay a theoretical foundation for the prediction on the vibration and sound radiation of more complicated particle-damping composite structures.