Dynamic stability of a damped nonlinear axially moving beam resting on the nonlinear elastic foundation

Ghulam Yameen  Mallah; Rajab Ali  Malookani; Muhammad Memon; Muzaffar Bashir Arain; Izhar Ali Amur

doi:10.59400/sv3381

Dynamic stability of a damped nonlinear axially moving beam resting on the nonlinear elastic foundation

Ghulam Yameen Mallah Department of Basic Science and Related Studies , Quaid-e-Awam University of Engineering, Science & Technology, Nawabshah 67480, Pakistan
Rajab Ali Malookani Department of Mathematics and Statistics, Quaid-e-Awam University Engineering, Science & Technology, Nawabshah 67480, Pakistan
Muhammad Memon Department of Basic Science and Related Studies , Quaid-e-Awam University of Engineering, Science & Technology, Nawabshah 67480, Pakistan
Muzaffar Bashir Arain Department of Mathematics and Statistics, Quaid-e-Awam University Engineering, Science & Technology, Nawabshah 67480, Pakistan
Izhar Ali Amur Department of Basic Science and Related Studies, Shaheed Benazir Bhutto University, Shaheed Benazirabad 67480, Pakistan

Article ID: 3381

DOI: https://doi.org/10.59400/sv3381

Keywords: axially moving beam; elastic foundation; viscous damping; two-time scales method; stability analysis

Abstract

The stability of nonlinear transverse vibrations of an axially moving beam resting on a nonlinear elastic foundation is analysed, considering the effects of viscous damping and a harmonically varying time-dependent velocity around a low constant mean speed. The beam is assumed to have simply supported boundary conditions at both ends. The contribution of this paper is the combined study of damping, nonlinear foundation, and harmonic velocity variation on the stability of axially moving beams, which has not been studied before. The governing equation for the transverse dynamics is a nonlinear partial differential equation with variable coefficients, which is solved using the two-timescale perturbation method in combination with the Fourier series method. The stability of the system is investigated for both non-resonant and resonant cases by examining the influence of key parameters, including nonlinear bending stiffness, nonlinear elastic foundation and damping. The analysis reveals that an increase in nonlinear bending stiffness and nonlinear elastic foundation tends to destabilize the system, leading to growing oscillations and instability. In contrast, an increase in damping enhances stability, causing oscillations to decay over time and leading to an asymptotically stable response. Furthermore, validation was carried out through comparison with an existing model.

Published

2025-08-29

How to Cite

Mallah, G. Y., Malookani, R. A., Memon, M., Arain, M. B., & Amur, I. A. (2025). Dynamic stability of a damped nonlinear axially moving beam resting on the nonlinear elastic foundation. Sound & Vibration, 59(4). https://doi.org/10.59400/sv3381

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Vol. 59 No. 4 (2025)

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

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