Effects of non-classical boundary conditions on the free vibration response of a cantilever Euler-Bernoulli beams

• Autorzy: Afras Abderrachid , El Ghoulbzouri Abdelouafi

Identyfikatory

DOI

10.29354/diag/158075

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

free vibration; natural frequency; boundary conditions; DTM; non-dimensional stiffness

PL

drgania swobodne; częstotliwość drgań; warunki brzegowe

• Wydawca: Polskie Towarzystwo Diagnostyki Technicznej
• Czasopismo: Diagnostyka
• Rocznik: 2023
• Tom: Vol. 24, No. 1
• Strony: art. no. 2023107
• Opis fizyczny: Bibliogr. 16 poz., rys., tab.

Twórcy

autor

Afras Abderrachid

• Laboratory of Applied Sciences, National School of Applied Sciences Al Hoceima, Tetouan, University Abdelmalek Essaadi, Morocco

autor

El Ghoulbzouri Abdelouafi

• Laboratory of Applied Sciences, National School of Applied Sciences Al Hoceima, Tetouan, University Abdelmalek Essaadi, Morocco

Bibliografia

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• 2. Raimondo Luciano, Hossein Darban, chiara Bartolomeo, Francesco Fabbrocino, Daniela Scorza. The free flexural vibrations of nanobeams with nonclassical boundary condition using stress-driven non local model for studied Mechanics Research Communication. 2020;107:103536. https://doi.org/10.1016/j.mechrescom.2020.103536.
• 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/10.1007/978-3-030-39062-4_15.
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• 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/10.1155/2017/1568019.
• 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/10.1080/15397734.2013.847778.
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• 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.2016.16636.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).