Volume 18, Issue 6 (10-2018)
Modares Mechanical Engineering 2018, 18(6): 61-68 |
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Ghasabi S A, Shahgholi M, Payghaneh G, Ahmadi M. Free and forced nonlinear vibrations analysis of a viscoelastic nano rotating beam by considering the surface effects. Modares Mechanical Engineering 2018; 18 (6) :61-68
URL: http://mme.modares.ac.ir/article-15-16124-en.html
URL: http://mme.modares.ac.ir/article-15-16124-en.html
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3- Head Of faculty Of Mechanical Engineering
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3- Head Of faculty Of Mechanical Engineering
Abstract: (7115 Views)
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.
Keywords: Nonlinear vibrations, free and forced vibrations, nano rotating beam, viscoelastic, surface effects
Article Type: Research Article |
Subject:
Aerospace Structures
Received: 2018/01/27 | Accepted: 2018/09/24 | Published: 2018/09/24
Received: 2018/01/27 | Accepted: 2018/09/24 | Published: 2018/09/24
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