1) Taniguchi, O. and Tamura, A.: Shin-pan Kogyo shindo gaku, CORONA PUBLISHING CO., LTD., pp.372-390, 1977 (In Japanese) 谷口修, 田村章義: 新版 工業振動学, コロナ社, pp.387-390, 1977
2) S.P. Timoshenko: On the correction for shear of the differential equation for transverse vibrations of prismatic bars, Philosophical Magazine and Journal of Science, Vol. 41, pp. 744-746, 1921
3) S.P. Timoshenko: On the transverse vibrations of bars of uniform cross-section, Philosophical Magazine and Journal of Science, Vol. 43, pp. 125-131, 1922
4) R.W. Traill-Nash and A.R. Collar: The effects of shear flexibility and rotatory inertia on the bending vibrations of beams, The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 6, pp. 186-222, 1953
5) T.C. Huang: The effect of rotatory inertia and of shear deformation on the frequency and normal mode equations of uniform beams with simple end conditions, Journal of Applied Mechanics, Vol. 28, No. 4, pp. 579-584, 1961
6) J.R. Hutchinson: Transverse vibrations of beams, exact versus approximate solutions, Journal of Applied Mechanics, Vol. 48, pp. 923-928, 1981
7) N.G. Stephen and S. Puchegger: On the valid frequency range of Timoshenko beam theory, Journal of Sound and Vibration, Vol. 297, pp. 1082-1087, 2006
8) Akiyama, K., Kishino, Y. and Murai, S.: Discussion on applicability of the Timoshenko beam theory based on the exact theory of wave propagation, Proceedings of JSCE A, Vol. 63, pp. 232-241, 2007 (in Japanese) 穐山和男, 岸野佑次, 村井貞規: 弾性波動論に基づくTimoshenkoはり理論の適用性の考察, 土木学会論文集A, Vol. 63, pp. 232-241, 2007
9) G.R. Bhashyam and G. Prathap: The second frequency spectrum of Timoshenko Beams, Journal of Sound and Vibration, Vol. 76, pp. 407-420, 1981
10) N.G. Stephen: The second frequency spectrum of Timoshenko beams, Journal of Sound and Vibration, Vol. 80, pp. 578-582, 1982
11) M. Levinson and D.W. Cooke: On the two frequency spectra of Timoshenko beams, Journal of Sound and Vibration, Vol. 84, pp. 319-326, 1982
12) V.V. Nesterenko: A theory for transverse vibrations of the Timoshenko beam, Journal of Applied Mathematics and Mechanics, Vol. 57, pp. 669-677, 1993
13) N.G. Stephen: The second frequency spectrum of Timoshenko beam theory-Further assessment, Journal of Sound and Vibration, No. 292, pp. 372-389, 2006
14) Chunfeng Wan, Rong Chen, Songtao Xue and Zhishen Wu: Development of a novel beam model and its dynamic characteristics, Mechanics of Advanced Materials and Structures, Vol. 22, pp. 402-412, 2015
15) Chunfeng Wan, Huachen Jiang, Liyu Xie, Caiqian Yang, Youliang Ding, Hesheng Tang and Songtao Xue: Natural frequency characteristics of the beam with different cross sections considering the shear deformation induced rotary inertia, Applied Sciences, Vol. 10, 5245, 2020
16) Komatsu, K. and Toda, S.: Beam-type vibrations of short thin cylindrical shells, Technical report of National Aerospace Laboratory, TR-502, 1977 (in Japanese) 小松敬治, 戸田勧: 円筒シェルの梁状曲げ振動について, 航空宇宙技術研究所報告, TR-502, 1977
17) R. Rahgozar, H. Safari and P. Kaviani: Free vibration of tall buildings using Timoshenko beams with variable cross-section, Structures Under Shock and Impact Ⅷ, Vol. 73, pp. 233-242, 2004
18) Mahdi Ebrahimian and Maria I. Todorovska: Wave propagation in a Timoshenko beam building model, Journal of Engineering Mechanics, Vol. 140, 040414018, 2014
19) Ming Hei Cheng and Thomas H. Heaton: Simulating building motions using ratios of the building’s natural frequencies and a Timoshenko beam model, Earthquake Spectra, Vol. 31, pp. 403-420, 2015
20) Tobe, T.: Kaiten kansei oyobi sendanryoku no eikyo wo koryo seru kin-itu danmen hari no yoko shindo ni tsuite, Transactions of the Japan Society of Mechanical Engineers, Vol.17, No.57, pp.14-19, 1951 (in Japanese) 戸部俊美: 回転慣性およびせん断力の影響を考慮せる均一断面はりの横振動について, 日本機械学会論文集, Vol. 17, No. 57, pp. 14-19, 1951
21) G.R. Cowper: The shear coefficient in Timoshenko’s beam theory, Journal of Applied Mechanics, Vol. 33, pp. 335-340, 1966
22) K. Sezawa: Die wirkung des enddruckes auf die biegungsschwingung eines stabes mit innerer dämpfung, ZAMM - Journal of Applied Mathematics and Mechanics, Vol. 12, pp. 275-279, 1932 (in German)
23) ABAQUS Analysis User’s Manual (v6.6), 23.3.3 Choosing a beam element, https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/usb/default.htm?startat=pt06ch23s03alm07.html (Reference date: 2021/ 04/ 10)