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Geomechanics and Engineering Volume 32, Number 2, January25 2023 , pages 125-135 DOI: https://doi.org/10.12989/gae.2023.32.2.125 |
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Nonlinear vibration analysis of carbon nanotube-reinforced composite beams resting on nonlinear viscoelastic foundation |
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M. Alimoradzadeh and and S.D. Akbas
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| Abstract | ||
| Nonlinear vibration analysis of composite beam reinforced by carbon nanotubes resting on the nonlinear viscoelastic foundation is investigated in this study. The material properties of the composite beam is considered as a polymeric matrix by reinforced carbon nanotubes according to different distributions. With using Hamilton's principle, the governing nonlinear partial differential equations are derived based on the Euler-Bernoulli beam theory. In the nonlinear kinematic assumption, the Von Kármán nonlinearity is used. The Galerkin' s decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then is solved by using of multiple time scale method. The nonlinear natural frequency and the nonlinear free response of the system is obtained. In addition, the effects of different patterns of reinforcement, linear and nonlinear damping coefficients of the viscoelastic foundation on the nonlinear vibration responses and phase trajectory of the carbon nanotube reinforced composite beam are investigated. | ||
| Key Words | ||
| carbon nanotubes; composite beams; nonlinear foundation; nonlinear vibration | ||
| Address | ||
| M. Alimoradzadeh: Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran S.D. Akbas: Department of Civil Engineering, Bursa Technical University, 16330, Bursa, Turkey | ||