Effects of non-classical boundary conditions on the free vibration response of a cantilever Euler-Bernoulli beams
| 1 | Laboratory of Applied Sciences, National School of Applied Sciences Al Hoceima,Tetouan, University Abdelmalek Essaadi, Morocco, |
CORRESPONDING AUTHOR
Abderrachid Afras
Laboratory of Applied Sciences, National School of Applied Sciences Al Hoceima,Tetouan, University Abdelmalek Essaadi, Morocco,
Laboratory of Applied Sciences, National School of Applied Sciences Al Hoceima,Tetouan, University Abdelmalek Essaadi, Morocco,
Submission date: 2022-08-13
Final revision date: 2022-10-19
Acceptance date: 2022-12-21
Online publication date: 2023-01-04
Publication date: 2023-01-04
Diagnostyka 2023;24(1):2023107
KEYWORDS
TOPICS
ABSTRACT
In this article, the problem of the free vibration behavior of a cantilever Euler-Bernoulli beam with various non-classical boundary conditions, such as rotational, translational spring, and attached mass is investigated. For describing the differential equation of the system. An analytical procedure is proposed firstly, and a numerical method based on the differential transform method DTM is developed in order to validate the obtained results. A parametric study for various degenerate cases is presented with the aim to analyze the influence of rotational stiffness, vertical stiffness, and mass ratio on the free vibration response of the beam, particularly on its modal characteristics. The results show that the non-classical boundary conditions significantly affect the natural frequency and mode shapes of the studied beam system in comparison to the case of a classical boundary conditions such as Simply supported, clamped-clamped, etc. The comparison between the obtained results based on the proposed analytical solution and numerical scheme, and those available in the literature shows an excellent agreement.
REFERENCES (16)
1.
Paulo J. Paupitz G, Michael J. Brennan, Andrew Peplow, Bin Tang. Calculation of the natural frequencies and mode shapes of an Euler–Bernoulli beam which has any combination of linear boundary conditions. Journal of vibration and control. 2019;25(18):2473–2479. https://doi.org/10.1177/107754....
2.
Raimondo Luciano, Hossein Darban, chiara Bartolomeo, Francesco Fabbrocino, Daniela Scorza. The free flexural vibrations of nanobeams with non-classical boundary condition using stress-driven non local model for studied Mechanics Research Communication. 2020;107:103536. https://doi.org/10.1016/j.mech....
3.
Lila Chalah-Rezgui, Chalah F, Chalah-Rezgui L, Djellab SE, Bali A. Vibration analysis of a uniform beam fixed at one end and restrained against translation and rotation at the second one. In: Öchsner A, Altenbach H. (eds) Engineering Design Applications III. Advanced Structured Materials. 2020;124.https://doi.org/10.1007/978-3-....
4.
Ding H, Zhu M, Chen L. Dynamic stiffness method for free vibration of an axially moving beam with generalized boundary conditions. Applied Mathematics and Mechanics -Engl. Ed. 2019;40:911–924. https://doi.org/10.1007/s10483....
5.
Sayed Mojtaba Hozhabrossadati. Exact solution for free vibration of elastically restrained cantilever non-uniform beams joined by a mass spring system at the free end. The IES Journal part A civil & structural Engineering. 2015;8(4):232–239. https://doi.org/10.1080/193732....
6.
Binghui Wang, Zhihua Wang and Xi Zuo. Frequency equation of flexural vibrating cantilever beam considering the rotary inertial moment of an attached mass. Mathematical Problems in Engineering: 2017:1568019. https://doi.org/10.1155/2017/1....
7.
Nuttawit Wattanasakulpong, Arisara Chaikittiratana. On the Linear and Nonlinear Vibration Responses of Elastically End Restrained Beams Using DTM, Mechanics Based Design of structures and Machines. 2014;42(2):135-150. https://doi.org/10.1080/153977....
8.
Kittisak Suddoung, Jarruwat charoensuk, Nuttawit Wattanasak-Kulpong. Application of the differential transformation method to vibration analysis of stepped beams with elastically constrained ends. Journal of vibration and control. 2012;19(16):2387–2400. https://doi.org/10.1177/107754....
9.
Dongyan Shi, Qingshan Wang, Xianjie Shi, Fuzhan pang. An accurate solution method for the vibration analysis of Timoshenko beams with general elastic supports. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. 2014;229 (13): 2327–2340. https://doi.org/10.1177/095440....
10.
Sayed Mojtaba Hozhabrossadati, Ahmed Aftabi Sani, Masood Mofid. Free vibration analysis of a beam with an intermediate sliding connection joined by a mass-spring system, Journal of vibration and control. 2016;22(04): 955–964. https://doi.org/10.1177/107754....
11.
Banerjee JR. Free vibration of beams carrying spring mass systems-a dynamic stiffness approach. Computers and Structures. 2012;104-105: 21-26. https://doi.org/10.1016/j.comp....
12.
Kim, HK, Kim, MS. Vibration of beams with generally restrained boundary conditions using fourier series. Journal Sound and vibration. 2001;245(5):771–784. https://doi.org/10.1006/jsvi.2....
13.
Lau, JH. Vibration frequencies and mode shapes for a constrained cantilever. Journal of Applied Mechanics. 1984;51:182–187. https://doi.org/10.1115/1.3167....
14.
Mohammed Darabi, Siavash Kazmirad, Mergen H. Ghayesh, MH. Free vibrations of beam-mass-spring systems: analytical analysis with numerical confirmation. Acta. Mechanica. Sinica. 2012;28:468–481. https://doi.org/10.1007/s10409....
15.
Fahy F and Walker J (eds). Advanced Applications in Acoustics, Noise and Vibration. London: Taylor & Francis. 2005. https://doi.org/10.1016/j.jsv.....
16.
Mustafa Özgür Yaylı, Süheyla Yerel Kandemir, Ali Erdem Çerçevik. A practical method for calculating eigenfrequencies of a cantilever micro-beam with the attached tip mass, Journal of Vibroengineering. 2016;18(5):3070-3077. https://doi.org/10.21595/jve.2....
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