NONLINEAR FORCED VIBRATION ANALYSIS OF FUNCTIONALLY GRADED NANOBEAMS IN THERMAL ENVIRONMENTS WITH CONSIDERING SURFACE STRESS AND NONLOCAL EFFECTS

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POURASHRAF SEYEDEH TALIEH; ANSARI REZA

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Journal: Modares Mechanical Engineering Year:2015 | Volume:14 | Issue:16 Page(s): 17-26

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Title

NONLINEAR FORCED VIBRATION ANALYSIS OF FUNCTIONALLY GRADED NANOBEAMS IN THERMAL ENVIRONMENTS WITH CONSIDERING SURFACE STRESS AND NONLOCAL EFFECTS

Author(s)

POURASHRAF SEYEDEH TALIEH | ANSARI REZA | Issue Writer Certificate

Keywords

FUNCTIONALLY GRADED NANOBEAMQ2

NONLINEAR FORCED VIBRATIONQ2

SURFACE STRESS EFFECTQ2

NONLOCAL EFFECTQ2

EXACT SOLUTIONQ2

Abstract

In this investigation, an EXACT SOLUTION is proposed for the NONLINEAR FORCED VIBRATION analysis of nanobeams made of functionally graded materials (FGMs) in thermal environment with considering the effects of surface stress and nonlocal elasticity theory. The physical properties of FGM nanobeams are assumed to vary through the thickness direction on the basis of the power law distribution. The geometrically nonlinear equations of motion and corresponding boundary conditions are derived using Hamilton’s principle on the basis of the Euler-Bernoulli beam theory. Using the Gurtin-Murdoch and Eringen elasticity theories, the surface stress and NONLOCAL EFFECTs are taken into account in obtained equations, respectively. For the solution purpose, first, the Galerkin procedure is employed in order to reduce the nonlinear partial differential governing equation into a nonlinear ordinary differential equation. This new equation is solved analytically by the multiple scales perturbation method. In the results section, the influences of different parameters including power law index, surface stress, nonlocal parameter, boundary conditions and temperature changes on the NONLINEAR FORCED VIBRATION response of nanobeams are investigated. Also, comparisons are made between the results obtained from the classical, Gurtin-Murdoch and Eringen elasticity theories. It is shown that as the thickness decreases, the SURFACE STRESS EFFECT moderates the hardening-type nonlinear behavior of nanobeams. This effect is more prominent at low magnitudes of thickness. Moreover, one can find that by increasing the nonlocal parameter, the hardening-type response of nanobeams is intensified.

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APA: Copy

POURASHRAF, SEYEDEH TALIEH, & ANSARI, REZA. (2015). NONLINEAR FORCED VIBRATION ANALYSIS OF FUNCTIONALLY GRADED NANOBEAMS IN THERMAL ENVIRONMENTS WITH CONSIDERING SURFACE STRESS AND NONLOCAL EFFECTS. MODARES MECHANICAL ENGINEERING, 14(16), 17-26. SID. https://sid.ir/paper/177888/en

Vancouver: Copy

POURASHRAF SEYEDEH TALIEH, ANSARI REZA. NONLINEAR FORCED VIBRATION ANALYSIS OF FUNCTIONALLY GRADED NANOBEAMS IN THERMAL ENVIRONMENTS WITH CONSIDERING SURFACE STRESS AND NONLOCAL EFFECTS. MODARES MECHANICAL ENGINEERING[Internet]. 2015;14(16):17-26. Available from: https://sid.ir/paper/177888/en

IEEE: Copy

SEYEDEH TALIEH POURASHRAF, and REZA ANSARI, “NONLINEAR FORCED VIBRATION ANALYSIS OF FUNCTIONALLY GRADED NANOBEAMS IN THERMAL ENVIRONMENTS WITH CONSIDERING SURFACE STRESS AND NONLOCAL EFFECTS,” MODARES MECHANICAL ENGINEERING, vol. 14, no. 16, pp. 17–26, 2015, [Online]. Available: https://sid.ir/paper/177888/en

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