轴向运动Timoshenko固支梁固有频率的数值仿真

张计光1,2，胡超荣1，唐有绮1,孟沥原3

doi:10.3969/j.issn.1007-2861.2011.05.014

上海大学学报(自然科学版) >

2011 , Vol. 17 >Issue 5: 648 - 652

DOI: https://doi.org/10.3969/j.issn.1007-2861.2011.05.014

数理化科学

轴向运动Timoshenko固支梁固有频率的数值仿真

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1.上海大学上海市应用数学和力学研究所，上海 200072; 2.日照职业技术学院，山东日照 276826; 3.同济大学物理系，上海 200092

收稿日期: 2010-05-31

网络出版日期: 2011-10-26

基金资助

上海市重点学科建设资助项目（S30106）；长江学者和创新团队发展计划基金资助项目（IRT0844）；上海大学创新基金资助项目(A.16-0401-08-005)

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Numerical Simulation of Natural Frequencies of Axially Moving Timoshenko Fixed Beams

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1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; 2. Rizhao Polytechnic, Rizhao 276826, Shandong, China; 3. Department of Physics, Tongji University, Shanghai 200092, China

Received date: 2010-05-31

Online published: 2011-10-26

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摘要

运用Galerkin方法和微分求积法求解固支边界轴向运动Timoshenko梁的固有频率.讨论系统的前两阶固有频率随轴向速度、刚度系数变化的情况，并将这2种方法得到的数值计算结果与复模态分析方法得到的精确解进行比较，发现用微分求积法和复模态分析法得到的结果几乎重合，而用Galerkin方法得到的结果在随刚度系数的增加和速度的增大时有所差异.

关键词： Galerkin方法; Timoshenko模型; 固有频率; 微分求积法; 轴向运动梁

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张计光1,2，胡超荣1，唐有绮1,孟沥原3 . 轴向运动Timoshenko固支梁固有频率的数值仿真[J]. 上海大学学报(自然科学版), 2011 , 17(5) : 648 -652 . DOI: 10.3969/j.issn.1007-2861.2011.05.014

Abstract

Natural frequencies of axially moving beams with fixed supports are analyzed based on the Timoshenko model by using the Galerkin method and the differential quadrature method. Numerical examples are presented to show effects of the related parameters on the frequencies, such as axial speed and stiffness. Results obtained with the differential quadrature and the complex mode methods are in good agreement, while the results obtained with the Galerkin method are slightly different.

Key words： axially moving beams; differential quadrature method; Galerkin method; natural frequencies; Timoshenko model

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