• Structural Engineering and Mechanics
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• 제73권1호
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• pp.37-52
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• 2020

This paper investigates the free and forced longitudinal vibration of a double nanorod system using doublet mechanics theory. The doublet mechanics theory is a multiscale theory spanning between lattice dynamics and continuum mechanics. Equations of motion and boundary conditions for the double nanorod system are obtained using Hamilton's principle. Clamped-clamped and clamped-free boundary conditions are considered. Frequencies and dynamic displacements are determined to demonstrate the effects of length scale parameter of considered material and geometry of the nanorods. It is shown that frequencies obtained by the doublet mechanics theory are bounded from above (van Hove singularity) and unlike classical elasticity theory doublet mechanics theory predicts finite number of modes depending on the length of the nanotube. The present doublet mechanics results have been compared to molecular dynamics, experimental and nonlocal theory results and good agreement is observed between the present and other mentioned results. The difference between wave frequencies of graphite is less than 10% between doublet mechanics and experimental results near to the end of the first Brillouin zone.

• Steel and Composite Structures
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• 제44권2호
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• pp.255-270
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• 2022

This manuscript illustrates the dynamic response of nanoscale carbon nanotubes (CNTs) embedded in an elastic media under moving load using doublet mechanics theory, which not considered before. CNTs are modelled by Timoshenko beam theory (TBT) and a bottom to up modelling nano-mechanics is simulated by doublet mechanics theory to capture the size effect of CNTs. To explore the influence of the CNTs configurations on the dynamic behaviour, both armchair and zigzag configurations are considered. The governing equations of motion and the associated boundary conditions are obtained using the Hamiltonian principle. The Navier solution methodology is applied to obtain the solutions for both orientations. Free vibration and forced response under moving loads are considered. The accuracy of the developed procedure is verified by comparing the obtained results with available previous algorithms and good agreement is observed. Parametric studies are conducted to demonstrate effects of doublet length scale, CNTs configurations, moving load velocities as well as the elastic media parameters on the dynamic behaviours of CNTs. The developed procedure is supportive in the design and manufacturing of MEMS/NEMS made from CNTs.

• Advances in nano research
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• 제15권5호
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• pp.411-422
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• 2023

In the present study, the axial vibration of the nanorods is investigated in the framework of the doublet mechanics theory. The equations of motion and boundary conditions of nanorods are derived by applying the Hamilton principle. A finite element method is developed to obtain the vibration frequencies of nanorods for different boundary conditions. A two-noded higher order rod finite element is used to solve the vibration problem. The natural frequencies of nanorods obtained with the present finite element analysis are validated by comparing the results of classical doublet mechanics and nonlocal strain gradient theories. The effects of rod length, mode number and boundary conditions on the axial vibration frequencies of nanorods are examined in detail. Mode shapes of the nanorods are presented for the different boundary conditions. It is shown that the doublet mechanics model can be used for the dynamic analysis of nanotubes, and the presented finite element formulation can be used for mechanical problems of rods with unavailable analytical solutions. These new results can also be used as references for the future studies.

• Smart Structures and Systems
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• 제26권2호
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• pp.213-226
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• 2020

In this manuscript, static and dynamic behaviors of geometrically imperfect carbon nanotubes (CNTs) subject to different types of end conditions are investigated. The Doublet Mechanics (DM) theory, which is length scale dependent theory, is used in the analysis. The Euler-Bernoulli kinematic and nonlinear mid-plane stretching effect are considered through analysis. The governing equation of imperfect CNTs is a sixth order nonlinear integro-partial-differential equation. The buckling problem is discretized via the differential-integral-quadrature method (DIQM) and then it is solved using Newton's method. The equation of linear vibration problem is discretized using DIQM and then solved as a linear eigenvalue problem to get natural frequencies and corresponding mode shapes. The DIQM results are compared with analytical ones available in the literature and excellent agreement is obtained. The numerical results are depicted to illustrate the influence of length scale parameter, imperfection amplitude and shear foundation constant on critical buckling load, post-buckling configuration and linear vibration behavior. The current model is effective in designing of NEMS, nano-sensor and nano-actuator manufactured by CNTs.

• 한국전산구조공학회논문집
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• 제18권4호통권70호
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• pp.453-458
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• 2005

본 논문은 연속체역학에서의 탄소성모델을 그대로 재현할 수 있는 미소구조모델에 관해서 연구하였다. 물체를 일정크기를 지닌 입자와 그 입자들을 연결하는 선형 스프링으로 모델링한 Doublet Mechanics를 기본이론으로 하여 이를 소성 영역으로 확장하였다. 그 결과로 가장 단순한 가정을 하였을 경우 미소모델과 연속체모델이 정확히 일대일 대응을 하는 것을 보였다. 2차원 평면응력문제에 대한 예제를 통해 미소변형률과 미소응력을 계산하였고 그 결과로 거동에 대해 분석하여 이 모델의 유효성을 입증하였다.