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Structural Engineering and Mechanics Volume 70, Number 6, June25 2019 , pages 737-750 DOI: https://doi.org/10.12989/sem.2019.70.6.737 |
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Energy equivalent model in analysis of postbuckling of imperfect carbon nanotubes resting on nonlinear elastic foundation |
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Nazira Mohamed, Mohamed A. Eltaher, Salwa A. Mohamed and Laila F. Seddek
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Abstract | ||
This paper investigates the static and dynamic behaviors of imperfect single walled carbon nanotube (SWCNT) modeled as a beam structure by using energy-equivalent model (EEM), for the first time. Based on EEM Young\'s modulus and Poisson\'s ratio for zigzag (n, 0), and armchair (n, n) carbon nanotubes (CNTs) are presented as functions of orientation and force constants. Nonlinear Euler-Bernoulli assumptions are proposed considering mid-plane stretching to exhibit a large deformation and a small strain. To simulate the interaction of CNTs with the surrounding elastic medium, nonlinear elastic foundation with cubic nonlinearity and shearing layer are employed. The equation governed the motion of curved CNTs is a nonlinear integro-partial-differential equation. It is derived in terms of only the lateral displacement. The nonlinear integro-differential equation that governs the buckling of CNT is numerically solved using the differential integral quadrature method (DIQM) and Newton\'s method. The linear vibration problem around the static configurations is discretized using DIQM and then is solved as a linear eigenvalue problem. Numerical results are depicted to illustrate the influence of chirality angle and imperfection amplitude on static response, buckling load and dynamic behaviors of armchair and zigzag CNTs. Both, clamped-clamped (C-C) and simply supported (SS-SS) boundary conditions are examined. This model is helpful especially in mechanical design of NEMS manufactured from CNTs. | ||
Key Words | ||
differential integral quadrature method; curved carbon nanotube; energy equivalent model; static post-buckling instability; linear vibration | ||
Address | ||
Nazira Mohamed, Salwa A. Mohamed and Laila F. Seddek : Department of Engineering Mathematics, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt Mohamed A. Eltaher: 1 Mechanical Engineering Dept., Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia 2 Mechanical Design & Production Dept., Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt | ||