基于Floquet理论的储液罐动力稳定性分析

为确定储液罐动力不稳定现象与激励参数间的关系,采用附加质量矩阵考虑流固耦合效应,以周期变化的几何刚度矩阵考虑壳体应力变化,由位移-压力格式的流固耦合方程建立储液罐在简谐地面加速度下的动力稳定性方程.利用模态截断法降阶上述方程,并基于Floquet理论求解,从而递归搜寻由激励参数描述的动力不稳定边界.利用上述Floquet方法分析Chiba试验模型,并基于B-R准则复核该结果.结果表明,Floquet方法求得的动力不稳定边界与Chiba试验较一致,并与B-R法结果吻合良好.Floquet方法可显著提高动力不稳定边界的求解效率,并消除壳体振型半波假定的影响.

Dynamic stability analysis of liquid storage tanks based on Floquet theory

To determine the relationship between dynamic instability phenomenon of liquid storage tanks and excitation parameters, from fluid-solid coupling equations with displacement-pressure form, the dynamic stability equations were established for liquid storage tanks under harmonic ground acceleration, in which the fluid-solid coupling effect was considered with added mass matrix and the shell stress change was considered with period-varying geometric stiffening matrix. After order reduction by modal truncation method, above equations were then solved based on Floquet theory to recursively search for the dynamic instability boundary described by the excitation parameters. The Chiba test models were analyzed by the proposed Floquet method, and the analysis results were reexamined based on B-R criterion. The results show that, the dynamic instability boundaries obtained by the Floquet method were consistent with Chiba test results, and agreed well with the estimates of B-R method. Floquet method can obviously improve the computational efficiency of dynamic instability boundary and eliminates the influence of half-wave assumption of shell vibration modes.