伽勒金方法与基于拉普拉斯的传递矩阵法相结合的悬臂流体输送管道动力学研究

IF 1.8 4区 工程技术 Q3 ENGINEERING, MECHANICAL
Jiang Liu, Qianli Zhao, Dongqi Wu
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引用次数: 0

摘要

本文提出了一种结合 Galerkin 离散化和 LTMM(基于拉普拉斯的传递矩阵法)的新型混合方法,用于研究具有潜在周期性和弹性支撑的悬臂流体输送管道的动力学。首先,通过 LTMM 回顾了由线性弹簧和扭转弹簧组合支撑的周期性悬臂梁的归一化模态函数推导。其次,通过 Galerkin 方法离散化了与前述梁具有相同材料和截面惯性矩的悬臂管的运动方程。然后,通过将获得的模态函数纳入 Galerkin 方法,提出了一种混合方法,简称 LTMM-Galerkin。第三,通过 LTMM-Galerkin 方法推导出特征函数和稳态位移响应。最后,进行了数值计算,并与传递矩阵法、有限差分法、微分正交法、格林函数法和微分变换法等现有方法进行了比较,验证了 LTMM-Galerkin 方法的有效性。LTMM-Galerkin 可与其他支持格式一起用于研究流体输送管道的动力学问题。此外,该方法的创建过程可作为其他混合方法的开发模型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Dynamics of cantilevered fluid-conveying pipes by Galerkin method combined with Laplace-based transfer matrix method

Dynamics of cantilevered fluid-conveying pipes by Galerkin method combined with Laplace-based transfer matrix method

A novel hybrid approach combining Galerkin discretization and LTMM (Laplace-based transfer matrix method) is put forward to study the dynamics of cantilevered fluid-conveying pipes possessing potential periodicity and elastic supports. Firstly, the deduction for normalized modal functions of a periodic cantilevered beam additionally supported by a combination of linear and torsional springs via LTMM is reviewed. Secondly, the motion equation for a cantilevered pipe with the same material and cross-section moment of inertia as the former-mentioned beam is discretized through the Galerkin method. A hybrid method, abbreviated as LTMM-Galerkin, is then proposed by incorporating the obtained modal functions into the Galerkin method. Thirdly, the eigenfunction and steady-state displacement response are deduced by LTMM-Galerkin. Finally, numerical calculations are carried out, and the validity of LTMM-Galerkin is verified compared with existed methods including transfer matrix method, finite difference method, differential quadrature method, Green function method, and differential transformation method. LTMM-Galerkin can be radiated to study dynamics problems of fluid-conveying pipes with other supporting formats. Additionally, the creation process of this method can serve as a model for the development of other hybrid approaches.

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来源期刊
CiteScore
3.60
自引率
13.60%
发文量
536
审稿时长
4.8 months
期刊介绍: The Journal of the Brazilian Society of Mechanical Sciences and Engineering publishes manuscripts on research, development and design related to science and technology in Mechanical Engineering. It is an interdisciplinary journal with interfaces to other branches of Engineering, as well as with Physics and Applied Mathematics. The Journal accepts manuscripts in four different formats: Full Length Articles, Review Articles, Book Reviews and Letters to the Editor. Interfaces with other branches of engineering, along with physics, applied mathematics and more Presents manuscripts on research, development and design related to science and technology in mechanical engineering.
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