薄壁圆柱壳在流体脉动激励下的振动特性分析

摘要：为深入研究薄壁圆柱壳在流体脉动激励下的运动特性，应用Donnell简化壳理论，考虑阻尼、结构非线性和附加质量的影响，建立了薄壁圆柱壳在流体脉动激励下的非线性振动方程。基于Galerkin方法将偏微分方程转化为方便求解的常微分方程，利用多尺度法求解了系统主共振的一次近似解，得到了系统稳态响应的转迁集与分岔图，并通过奇异性分析，得到了系统工作稳定性和可靠性的结构参数区域。对薄壁圆柱壳在流体作用下的振动特性进行了数值模拟和实验研究，考察了阻尼系数、脉动频率、液体深度等对系统动力学特性的影响。研究表明，考虑阻尼、结构非线性和附加质量的非线性振动方程更能体现薄壁圆柱壳在流体脉动激励下完整的动力学特性，同时系统中存在多种分岔行为。

Vibration characteristic analysis of thin cylindrical shell excited by pulsating flow

In order to further research the characteristics of thin cylindrical shell excited by pulsating flow,considering the influences of damping,geometric nonlinearity and added mass,a nonlinear vibration equation under pulsating flow excitation was established by using Donnell’s shallow-shell theory.The partial differential equation was transformed into an ordinary differential equation by using Galerkin method.By means of the method of multiple scales,the first approximate solution of the primary resonance of the system was acquired.The transition variety and bifurcation diagram in the unfolding parametric plane were given,the singularity and stability of the system were analysed and the stable regions of structural parameters were achieved.Experiments and numerical simulations were accomplished to study the impact of system parameters,such as the damping the pulsating frequency,the depth of liquid,etc..The results show that the nonlinear vibration equation presented in the paper is better to reflect the dynamic characteristics,and various bifurcation behaviors existing in the system are well explained.