Nonlinear vibrations in homogeneous non-prismatic Timoshenko cantilevers

Navadeh, Navid; Sareh, Pooya; Basovsky, Vladimir G.; Gorban, Irina M.; Soleiman Fallah, Arash

doi:10.1115/1.4051820

Publication type:	Article in scientific journal
Type of review:	Not specified
Title:	Nonlinear vibrations in homogeneous non-prismatic Timoshenko cantilevers
Authors:	Navadeh, Navid Sareh, Pooya Basovsky, Vladimir G. Gorban, Irina M. Soleiman Fallah, Arash
et. al:	No
DOI:	10.1115/1.4051820
Published in:	Journal of Computational and Nonlinear Dynamics
Volume(Issue):	16
Issue:	10
Issue Date:	17-Jul-2021
Publisher / Ed. Institution:	The American Society of Mechanical Engineers
ISSN:	1555-1415 1555-1423
Language:	English
Subject (DDC):	530: Physics 624: Civil engineering
Abstract:	Deep cantilever beams, modelled using Timoshenko beam kinematics, have numerous applications in engineering. This study deals with the nonlinear dynamic response in a non-prismatic Timoshenko beam characterized by considering the deformed configuration of the axis. The mathematical model is derived using the extended Hamilton's principle under the condition of finite deflections and angles of rotation. The discrete model of the beam motion is constructed based on the finite difference method (FDM), whose validity is examined by comparing the results for a special case with the corresponding data obtained by commercial finite element (FE) software ABAQUS 2019. The natural frequencies and vibration modes of the beam are computed. These results demonstrate decreasing eigenfrequency in the beam with increasing amplitudes of nonlinear oscillations. The numerical analyses of forced vibrations of the beam show that its points oscillate in different manners depending on their relative position along the beam. Points close to the free end of the beam are subject to almost harmonic oscillations, and the free end vibrates with a frequency equal to that of the external force. When a point approaches the clamped end of the beam, it oscillates in two-frequency mode and lags in phase from the oscillations of the free end. The analytical model allows for the study of the influence of each parameter on the eigenfrequency and the dynamic response. In all cases, a strong correlation exists between the results obtained by the analytical model and ABAQUS, nonetheless, the analytical model is computationally less expensive.
URI:	http://hdl.handle.net/10044/1/90501 https://digitalcollection.zhaw.ch/handle/11475/22914
Fulltext version:	Published version
License (according to publishing contract):	Licence according to publishing contract
Departement:	School of Engineering
Organisational Unit:	Institute of Computational Physics (ICP)
Appears in collections:	Publikationen School of Engineering

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Navadeh, N., Sareh, P., Basovsky, V. G., Gorban, I. M., & Soleiman Fallah, A. (2021). Nonlinear vibrations in homogeneous non-prismatic Timoshenko cantilevers. Journal of Computational and Nonlinear Dynamics, 16(10). https://doi.org/10.1115/1.4051820

Navadeh, N. et al. (2021) ‘Nonlinear vibrations in homogeneous non-prismatic Timoshenko cantilevers’, Journal of Computational and Nonlinear Dynamics, 16(10). Available at: https://doi.org/10.1115/1.4051820.

N. Navadeh, P. Sareh, V. G. Basovsky, I. M. Gorban, and A. Soleiman Fallah, “Nonlinear vibrations in homogeneous non-prismatic Timoshenko cantilevers,” Journal of Computational and Nonlinear Dynamics, vol. 16, no. 10, Jul. 2021, doi: 10.1115/1.4051820.

NAVADEH, Navid, Pooya SAREH, Vladimir G. BASOVSKY, Irina M. GORBAN und Arash SOLEIMAN FALLAH, 2021. Nonlinear vibrations in homogeneous non-prismatic Timoshenko cantilevers. Journal of Computational and Nonlinear Dynamics [online]. 17 Juli 2021. Bd. 16, Nr. 10. DOI 10.1115/1.4051820. Verfügbar unter: http://hdl.handle.net/10044/1/90501

Navadeh, Navid, Pooya Sareh, Vladimir G. Basovsky, Irina M. Gorban, and Arash Soleiman Fallah. 2021. “Nonlinear Vibrations in Homogeneous Non-Prismatic Timoshenko Cantilevers.” Journal of Computational and Nonlinear Dynamics 16 (10). https://doi.org/10.1115/1.4051820.

Navadeh, Navid, et al. “Nonlinear Vibrations in Homogeneous Non-Prismatic Timoshenko Cantilevers.” Journal of Computational and Nonlinear Dynamics, vol. 16, no. 10, July 2021, https://doi.org/10.1115/1.4051820.