DataVXApplied SciencesPaper
journal article·2020-07-29Open access

Natural Frequency Characteristics of the Beam with Different Cross Sections Considering the Shear Deformation Induced Rotary Inertia

Chunfeng Wan, Huachen Jiang, Liyu Xie, Caiqian Yang, Youliang Ding, Hesheng Tang, Songtao Xue

Applied Sciences· Volume 10· Issue 15
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Source abstract

Abstract

Based on the classical Timoshenko beam theory, the rotary inertia caused by shear deformation is further considered and then the equation of motion of the Timoshenko beam theory is modified. The dynamic characteristics of this new model, named the modified Timoshenko beam, have been discussed, and the distortion of natural frequencies of Timoshenko beam is improved, especially at high-frequency bands. The effects of different cross-sectional types on natural frequencies of the modified Timoshenko beam are studied, and corresponding simulations have been conducted. The results demonstrate that the modified Timoshenko beam can successfully be applied to all beams of three given cross sections, i.e., rectangular, rectangular hollow, and circular cross sections, subjected to different boundary conditions. The consequence verifies the validity and necessity of the modification.
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Research context

OpenAlex topics: Composite Structure Analysis and Optimization · Vibration and Dynamic Analysis · Dynamics and Control of Mechanical Systems

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Key Laboratory of Concrete and Prestressed Concrete Structure of Ministry of Education, Southeast University, Nanjing 210096, China

Research Institute of Structural Engineering and Disaster Reduction, College of Civil Engineering, Tongji University, Shanghai 200092, China

College of Civil Engineering & Mechanics, Xiangtan University, Xiangtan 411105, China

Department of Architecture, Tohoku Institute of Technology, Sendai, Miyagi 982-8577, Japan

Funding

Innovative Venture Technology Investment Project of Hunan Province · National Key Research and Development Program of China · Distinguished Young Scientists of Jiangsu Province · National Natural Science Foundation of China

References (22)

Show source-provided references
1. Timoshenko, S.P. (1953). History of Strength of Materials, Dover Publications.
2. Strutt, J.W. (1877). Theory of Sound, Macmillan Publications Co.
3. The second frequency spectrum of Timoshenko beams10.1016/S0022-460X(77)80118-1 ↗
4. On the correction for shear of the differential equation for transverse vibrations of bars of uniform cross-section10.1080/14786442108636264 ↗
5. On the transverse vibrations of bars of uniform cross-section10.1080/14786442208633855 ↗
6. The effects of shear flexibility and rotatory inertia on the bending vibrations of beams
7. On the Timoshenko theory of transverse beam vibrations10.1090/qam/62620 ↗
8. Forced motions of Timoshenko beams10.1115/1.4010969 ↗
9. Boley, B.A., and Chao, C.C. (1954). Some Solutions of the Timoshenko Beam Equations, Department of Civil Engineering and Engineering Mechanics, Institute of Air Flight Structures, Columbia University.
10. The effect of rotatory inertia and of shear deformation on the frequency and normal mode equations of uniform beams with simple end conditions10.1115/1.3641787 ↗
11. Reismann, H., and Pawlik, P.S. (1974). Elastokinetics, West Publishing Co.
12. Flexural vibrations in uniform beams according to the Timoshenko theory10.1115/1.4010755 ↗
13. Transverse vibration of a uniform, simply supported Timoshenko beam without transverse deflection
14. On the two frequency spectra of Timoshenko beams10.1016/0022-460X(82)90480-1 ↗
15. Finite element model for dynamic analysis of Timoshenko beam10.1016/S0022-460X(75)80176-3 ↗
16. On the variation of Timoshenko’s shear coefficient with frequency10.1115/1.3424391 ↗
17. Timoshenko’s shear coefficient from a beam subjected to gravity loading10.1115/1.3153589 ↗
18. The second spectrum of Timoshenko beam theory—Further assessment10.1016/j.jsv.2005.08.003 ↗
19. Exact solution of the bending vibration problem of FGM beams with variation of material properties10.1016/j.engstruct.2010.02.010 ↗
20. Wan, C. (2003). The Modification of Motion Equation of Timoshenko Beam and Its Application in Impact Responses of Structures. [Master thesis, Tongji University]. (In Chineses).
21. Development of a novel beam model and its dynamic characteristics
22. Modification of motion equation of Timoshenko beam and Its effect