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Analysis of Beam Transverse Vibration with Elastic Cubic Nonlinearity

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Abstract:

The dynamic nonlinear behavior of a beam, which is modeled as mass-spring mechanical systems, is the main subject of this investigation. Unlike most previous research that considers homogeneous and uniform beams, the findings of this research hold significant developments for the nonlinear vibration of non-homogeneous beams, which can be described as a bar-helical spring system. In this system, the mass of each bar changes over the length of the beam according to the local mass density of the non-homogeneous beam. The five-degree-of-freedom mass-spring model used in this paper can also be expanded to multi-degrees-of-freedom or even to a continuous system. The nonlinear beam response is investigated for three situations of increasing mass density and contrasted with its influence on dynamic features such as amplitudes, mode shapes, and natural frequencies. Therefore, three cases of mass distribution are considered for both symmetric and asymmetric nonlinear stiffness. Results are given as plots of vibration amplitude versus non-dimensional natural frequency for various cases of mass distribution. Obtained results underscore how mass density and stiffness symmetry critically influence the nonlinear beam dynamic response.

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Periodical:

Construction Technologies and Architecture (Volume 21)

Pages:

65-78

DOI:

https://doi.org/10.4028/p-jkGDH6

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Online since:

January 2026

Authors:

Mohamed Janati*, Lmokhtar Ikhharrazne, Mustapha Lamine

Keywords:

Cubic Nonlinearity, Explicit Method, Five Degrees of Freedom System, Hamilton’s Principle, Influence of Mass Change, Nonlinear Vibration of Beams, Spectral Analysis

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© 2026 Trans Tech Publications Ltd. All Rights Reserved

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