Free and forced nonlinear vibrations analysis of a viscoelastic nano rotating beam by considering the surface effects

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Ghasabi S. Ali; SHAHGHOLI MAJID; Payghaneh Gholamhasan; AHMADI GHOMI MOHAMMAD ALI

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Journal: Modares Mechanical Engineering Year:2018 | Volume:18 | Issue:6 Page(s): 61-68

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Title

Free and forced nonlinear vibrations analysis of a viscoelastic nano rotating beam by considering the surface effects

Author(s)

Ghasabi S. Ali | SHAHGHOLI MAJID | Payghaneh Gholamhasan | AHMADI GHOMI MOHAMMAD ALI | Issue Writer Certificate

Keywords

Nonlinear vibrationsQ2

free and forced vibrationsQ1

nano rotating beamQ1

viscoelasticQ1

surface effectsQ1

Abstract

In this paper free and forced vibrations analysis of a viscoelastic nonlinear nano rotating beam by considering surface effects is investigated. Using Hamilton principle and Gurtin Murdoch theory, the equations of motion are obtained and discretized by Galerkin method. Using the multiple time scales method the equations of motion are solved. In free vibrations analysis, the analytical expressions for amplitude and phase are obtained. In forced vibrations analysis the steady state solution are obtained. The effect of surface effect, damping coefficients, dimensions of cross section area, external excitation amplitude etc. on frequency response curves are investigated. It is seen that in free vibrations, by increasing surface stress the amplitude of the system decreased, and by increasing surface density or elasticity it is increased. Also, by increasing internal and external damping coefficients free vibration amplitude is decreased. In forced vibrations, it is seen that considering surface effect the amplitude of the system is decreased and the first bifurcation point is obviously changed. By increasing internal and external damping coefficients the amplitude is decreased and the first bifurcation point occur in frequencies near the natural frequency. It is seen that for two different dimensions of cross section with same area, amplitude and the loci of the bifurcation points are changed. By increasing the amplitude of external excitation the amplitude of response is increased the bifurcation points occur in frequencies far away from natural frequency. So, considering the surface effects for free and forced vibrations analysis of the nano rotating beams is mandatory.

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APA: Copy

Ghasabi, S. Ali, SHAHGHOLI, MAJID, Payghaneh, Gholamhasan, & AHMADI GHOMI, MOHAMMAD ALI. (2018). Free and forced nonlinear vibrations analysis of a viscoelastic nano rotating beam by considering the surface effects. MODARES MECHANICAL ENGINEERING, 18(6 ), 61-68. SID. https://sid.ir/paper/178101/en

Vancouver: Copy

Ghasabi S. Ali, SHAHGHOLI MAJID, Payghaneh Gholamhasan, AHMADI GHOMI MOHAMMAD ALI. Free and forced nonlinear vibrations analysis of a viscoelastic nano rotating beam by considering the surface effects. MODARES MECHANICAL ENGINEERING[Internet]. 2018;18(6 ):61-68. Available from: https://sid.ir/paper/178101/en

IEEE: Copy

S. Ali Ghasabi, MAJID SHAHGHOLI, Gholamhasan Payghaneh, and MOHAMMAD ALI AHMADI GHOMI, “Free and forced nonlinear vibrations analysis of a viscoelastic nano rotating beam by considering the surface effects,” MODARES MECHANICAL ENGINEERING, vol. 18, no. 6 , pp. 61–68, 2018, [Online]. Available: https://sid.ir/paper/178101/en

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