Dynamics of a beam-column element on an elastic foundation

This paper proposes a novel nanobar–substrate medium model for static and free vibration analyses of single-walled carbon nanotube (SWCNT) systems embedded in the elastic substrate medium. The modified strain-gradient elasticity theory is utilized to account for the material small-scale effect, while the Gurtin–Murdoch surface theory is employed to represent the surface energy effect. The Winkler foundation model is assigned to consider the interactive mechanism between the nanobar and its surrounding substrate medium. Hamilton’s principle is used to consistently derive the system governing equation, initial conditions, and classical as well as non-classical boundary conditions. Two numerical simulations are employed to demonstrate the essence of the material small-scale effect, the surface energy effect, and the surrounding substrate medium on static and free vibration responses of single-walled carbon nanotube (SWCNT)–substrate medium systems. The simulation results show that the material small-scale effect, the surface energy effect, and the interaction between the substrate and the structure led to a system-stiffness enhancement both in static and free vibration analyses.

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“…As suggested by Dinçkal et al [ 61 ], there are two possible solution cases for the non-trivial solution,

:…”

Section: Nanobar–substrate Medium Model: Single-walled Carbon Nanotub...mentioning

confidence: 99%

Static and Free Vibration Analyses of Single-Walled Carbon Nanotube (SWCNT)–Substrate Medium Systems

et al. 2022

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“…Only Timoshenko beam theory has been used in these studies. Furthermore some researchers [25][26][27][28][29][30][31] have employed finite element as a tool in analyzing the effects of vibration of many structures. Neither of these studies has obtained analytical solutions for vibration of nano-beams based on nonlocal Euler-Bernoulli beam theory with considering both effects of initial stress and small length scale for all boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Vibration of Initially Stressed Nonlocal Euler-Bernoulli Nano-Beams

Dinçkal¹

2018

Academic Platform-Journal of Engineering and Science

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This paper is pertinent to the analytical solutions for vibration analysis of initially stressed Nonlocal Euler-Bernoulli nano-beams. In order to take into account of small length scale effect, this vibration problem formulation is depending upon both nonlocal Euler-Bernoulli and also Eringen's nonlocal elasticity theory. The boundary conditions and governing equation are obtained by use of Hamiltonian's principle. These equations are solved analytically with different initial stresses (both compressive and tensile) and boundary conditions. The effect of small length scale and the initial stress on the fundamental frequency are investigated. The solutions obtained are compared with the ones depending upon both classical Euler-Bernoulli and Timoshenko beam theory to comprehend the responses of nanobeams under the effect of initial stress and small scale in terms of frequencies for both theories. The results supply a better declaration for vibration analysis of nano-beams which are short and stubby with initial stress.

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Dynamics of a beam-column element on an elastic foundation

Cited by 2 publications

References 17 publications

Static and Free Vibration Analyses of Single-Walled Carbon Nanotube (SWCNT)–Substrate Medium Systems

Static and Free Vibration Analyses of Single-Walled Carbon Nanotube (SWCNT)–Substrate Medium Systems

Vibration of Initially Stressed Nonlocal Euler-Bernoulli Nano-Beams

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