CHAOTIC BEHAVIOR OF NONLOCAL NANOBEAM RESTING ON A NONLINEAR VISCOELASTIC FOUNDATION SUBJECTED TO HARMONIC EXCITATION

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MIR MASSOUD; TAHANI MASOUD

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Journal: Modares Mechanical Engineering Year:2018 | Volume:18 | Issue:2 Page(s): 264-272

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Title

CHAOTIC BEHAVIOR OF NONLOCAL NANOBEAM RESTING ON A NONLINEAR VISCOELASTIC FOUNDATION SUBJECTED TO HARMONIC EXCITATION

Author(s)

MIR MASSOUD | TAHANI MASOUD | Issue Writer Certificate

Keywords

NANOBEAMQ2

NONLOCAL ELASTICITYQ1

VISCOELASTIC FOUNDATIONQ1

CHAOSQ1

MELNIKOV ANALYSISQ1

Abstract

In this paper, the nonlinear vibration of a Euler–Bernoulli NANOBEAM resting on a non-linear VISCOELASTIC FOUNDATION is investigated. It is assumed that the NANOBEAM is subjected to a harmonic excitation that can be representative of an electrostatic field. The non-linear VISCOELASTIC FOUNDATION is considered for both hardening and softening cases. By neglecting of the in-plane inertia, Eringen's NONLOCAL ELASTICITY theory is used to model and derive the equation of motion of the NANOBEAM. Using the Galerkin method and the first mode shape, the obtained partial differential equation is reduced to the ordinary differential equation. Calculating the system's equilibrium points lead to heteroclinic bifurcation and the heteroclinic orbits are obtained. Then, using the Melnikov integral method, the chaotic motion of the system is studied analytically, and the safe region of the system is determined respect to the parametric space of the problem. When the VISCOELASTIC FOUNDATION has a hardening characteristic, the chaotic behavior in the system does not occur. It has been observed that the use of NONLOCAL ELASTICITY theory is necessary to investigate the chaotic behavior of NANOBEAM, and using the classical theory of elasticity may place the system in the chaotic region.

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APA: Copy

MIR, MASSOUD, & TAHANI, MASOUD. (2018). CHAOTIC BEHAVIOR OF NONLOCAL NANOBEAM RESTING ON A NONLINEAR VISCOELASTIC FOUNDATION SUBJECTED TO HARMONIC EXCITATION. MODARES MECHANICAL ENGINEERING, 18(2 ), 264-272. SID. https://sid.ir/paper/178675/en

Vancouver: Copy

MIR MASSOUD, TAHANI MASOUD. CHAOTIC BEHAVIOR OF NONLOCAL NANOBEAM RESTING ON A NONLINEAR VISCOELASTIC FOUNDATION SUBJECTED TO HARMONIC EXCITATION. MODARES MECHANICAL ENGINEERING[Internet]. 2018;18(2 ):264-272. Available from: https://sid.ir/paper/178675/en

IEEE: Copy

MASSOUD MIR, and MASOUD TAHANI, “CHAOTIC BEHAVIOR OF NONLOCAL NANOBEAM RESTING ON A NONLINEAR VISCOELASTIC FOUNDATION SUBJECTED TO HARMONIC EXCITATION,” MODARES MECHANICAL ENGINEERING, vol. 18, no. 2 , pp. 264–272, 2018, [Online]. Available: https://sid.ir/paper/178675/en

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