Natural dynamic characteristics of a circular cylindrical Timoshenko tube made of three-directional functionally graded material

doi:10.1007/s10483-022-2839-6

Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (4): 479-496.doi: https://doi.org/10.1007/s10483-022-2839-6

Natural dynamic characteristics of a circular cylindrical Timoshenko tube made of three-directional functionally graded material

Ye TANG^1,2, Jiye XU¹, Tianzhi YANG³

1. School of Mechanical Engineering, Anhui Polytechnic University, Wuhu 241000, Anhui Province, China;
2. Department of Mechanics, Tianjin University, Tianjin 300350, China;
3. School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China

收稿日期:2021-12-13 修回日期:2022-01-28 发布日期:2022-03-29
通讯作者: Tianzhi YANG, E-mail:yangtianzhi@me.neu.edu.cn
基金资助:
the National Natural Science Foundation of China (Nos. 11902001 and 12072221), the China Postdoctoral Science Foundation (No. 2018M641643), and the Anhui Provincial Natural Science Foundation of China (Nos.1908085QA13 and 1808085ME128)

Natural dynamic characteristics of a circular cylindrical Timoshenko tube made of three-directional functionally graded material

Ye TANG^1,2, Jiye XU¹, Tianzhi YANG³

1. School of Mechanical Engineering, Anhui Polytechnic University, Wuhu 241000, Anhui Province, China;
2. Department of Mechanics, Tianjin University, Tianjin 300350, China;
3. School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China

Received:2021-12-13 Revised:2022-01-28 Published:2022-03-29
Contact: Tianzhi YANG, E-mail:yangtianzhi@me.neu.edu.cn
Supported by:
the National Natural Science Foundation of China (Nos. 11902001 and 12072221), the China Postdoctoral Science Foundation (No. 2018M641643), and the Anhui Provincial Natural Science Foundation of China (Nos.1908085QA13 and 1808085ME128)

摘要/Abstract

摘要： The natural dynamic characteristics of a circular cylindrical tube made of three-directional (3D) functional graded material (FGM) based on the Timoshenko beam theory are investigated. Hamilton’s principle is utilized to derive the novel motion equations of the tube, considering the interactions among the longitudinal, transverse, and rotation deformations. By dint of the differential quadrature method (DQM), the governing equations are discretized to conduct the analysis of natural dynamic characteristics. The Ritz method, in conjunction with the finite element method (FEM), is introduced to verify the present results. It is found that the asymmetric modes in the tube are controlled by the 3D FGM, which exhibit more complicated shapes compared with the unidirectional (1D) and bi-directional (2D) FGM cases. Numerical examples illustrate the effects of the axial, radial, and circumferential FGM indexes as well as the supported edges on the natural dynamic characteristics in detail. It is notable that the obtained results are beneficial for accurate design of smart structures composed from multi-directional FGM.

关键词: circular cylindrical tube, three-directional (3D) functionally graded material (FGM), asymmetric mode, natural dynamic characteristic, differential quadrature method (DQM)

Abstract: The natural dynamic characteristics of a circular cylindrical tube made of three-directional (3D) functional graded material (FGM) based on the Timoshenko beam theory are investigated. Hamilton’s principle is utilized to derive the novel motion equations of the tube, considering the interactions among the longitudinal, transverse, and rotation deformations. By dint of the differential quadrature method (DQM), the governing equations are discretized to conduct the analysis of natural dynamic characteristics. The Ritz method, in conjunction with the finite element method (FEM), is introduced to verify the present results. It is found that the asymmetric modes in the tube are controlled by the 3D FGM, which exhibit more complicated shapes compared with the unidirectional (1D) and bi-directional (2D) FGM cases. Numerical examples illustrate the effects of the axial, radial, and circumferential FGM indexes as well as the supported edges on the natural dynamic characteristics in detail. It is notable that the obtained results are beneficial for accurate design of smart structures composed from multi-directional FGM.

Key words: circular cylindrical tube, three-directional (3D) functionally graded material (FGM), asymmetric mode, natural dynamic characteristic, differential quadrature method (DQM)

中图分类号:

74F05

Ye TANG, Jiye XU, Tianzhi YANG. Natural dynamic characteristics of a circular cylindrical Timoshenko tube made of three-directional functionally graded material[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(4): 479-496.

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Natural dynamic characteristics of a circular cylindrical Timoshenko tube made of three-directional functionally graded material

Natural dynamic characteristics of a circular cylindrical Timoshenko tube made of three-directional functionally graded material

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