摘要
将欧拉-伯努利梁和平推流理论分别用于描述细长输流管路的力学模型及其内部的流体流动模型,利用格林函数法推导了固定-弹性支承式输流管路的格林函数,并得到了挠度的解析表达式。分别分析管路的挠度与激振位置,激振频率,内部流体的流速,弹簧的刚度系数以及质量比的关系。在给定数据的基础上,利用格林函数法计算得到了临界激振位置的具体数值。在分析激振频率对挠度影响的同时求解了管路的固有频率并与微分变换法的解作了对比,发现格林函数法具有较高的精度。方法可推广至研究任意支承形式,多个激励的强迫振动问题。研究内容可为后续的可靠性设计提供精确的计算结果,为设计人员提供方法上的指导。
Euler-Bernoulli beam and plug flow theories are adopted to describe the mechanical model of slender fluid-conveying pipe and internal fluid flow model separately. Green＇s function method（GFM） is used to derive the Green＇s function of the fixedelastically supported fluid-conveying pipe, sequentially, and the analytical expression of deflection is obtained. The relationships between deflection and exciting position, exciting frequency, velocity of internal fluid, stiffness coefficient of spring and mass ratio are investigated respectively. Critical excitation position is calculated out based on the given data by means of GFM. During the analytical process of the influence of excitation frequency on deflection, GFM is used to solve the natural frequency simultaneously and results are compared with that of differential transformation method（DTM）, as a result, GFM is found to be accurate enough. The proposed method can be expanded to study the forced vibration problems with arbitrary kind of support or multiple excitation forces. Research contents can provide accurate results for further reliability design and methodological reference for designers.
出处
《机械工程学报》
EI
CAS
CSCD
北大核心
2017年第12期186-191,共6页
Journal of Mechanical Engineering
基金
国家科技重大专项资助项目(2013ZX04011011)
关键词
输流管路
强迫振动
格林函数法
挠度
fluid-conveying pipe
forced vibration
Green＇s function method
deflection
