非线性输流曲管面内振动的样条小波有限元方法研究  

Wavelet-based finite element method for the nonlinear in-plane vibration of curved pipes conveying fluid

作　　者：曹建华 黄颖青[2] 仝国军 赵年顺 CAO Jianhua;HUANG Yingqing;TONG Guojun;ZHAO Nianshun(The School of Mechanicaland Electrical Engineering,Huangshan University,Huangshan 245021,China;Department of Modern Mechanics,School of Engineering and Science,University of Science and Technology of China,Hefei 230026,China;Key Laboratory of Geotechnical Engineering Safety and Deformation Control,Hebei University of Water Resources and Electric Engineering,Cangzhou 061001,China)

机构地区：[1]黄山学院机电工程学院,安徽黄山245021 [2]中国科学技术大学工程科学学院近代力学系,合肥230027 [3]河北水利电力学院岩土工程安全与变形控制重点实验室,河北沧州061001

出　　处：《振动与冲击》2022年第18期66-74,103,共10页Journal of Vibration and Shock

基　　金：高校优秀青年人才支持计划(gxyq2020053,gxyq2020052);安徽省仿真设计与现代制造工程技术研究中心开放研究项目(SGCZXYB1802);2021年中国科学技术大学同步辐射联合基金;黄山学院人才启动项目(2020xkjq002)。

摘　　要：由于小波具有多尺度和多分辨等优点,小波有限元的研究和应用受到越来越多的关注。以轴线可伸长的非线性输流曲管为研究对象,详述推导其面内振动微分方程的过程,采用尺度为3、阶数为4和尺度为2、阶数为3的区间样条小条尺度函数分别作为曲管径向位移和周向位移的插值函数,建立了输流曲管面内振动的区间样条小波曲管单元,并应用小波有限元离散了其微分方程,求解了输流曲管的频率、模态和时域响应。数值结果表明:小波有限元计算的前3阶频率与文献对比的误差不超过0.306%,曲管模态基本相似,而在时域动力响应计算上,小波有限元的数值结果与传统有限元几乎重合,且小波有限元频率和时域动力响应的计算时间均大幅减少。以上结论均表明小波有限元在非线性输流曲管面内振动计算有着一定的优势。Because of the advantages of multi-scale and multi-resolution,the research and application of wavelet-based finite element method have attracted more and more attention.The vibration of a nonlinear curved pipe conveying fluid was studied,and the differential equation of in-plane vibration of the curved pipe conveying fluid was derived in detail.In order to construct the wavelet-based finite element,the interval spline scale function with scale 3,order 4 and scale 2,order 3 were used as the interpolation functions of radial and circumferential displacements respectively.The differential equations of the fluid-conveying curved pipe were discretized by the wavelet-based finite elements,and the frequencies,modals and time history of the curved pipe were calculated.The numerical results show that the frequency calculated by the wavelet-based finite element method is almost the same as that in the literature,as well as the modes of the curved pipe.Moreover,the dynamic responses at middle node are almost the same as those by the traditional finite element,method,while the calculation time is shorter.The above conclusions show that the wavelet-based finite element method has certain advantages in the calculation of the in-plane vibration of nonlinear curved pipes.

关 键 词：非线性 曲管 小波有限元 样条小波 

分 类 号：O321[理学—一般力学与力学基础] O327[理学—力学]