• 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.

• 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.

• 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.

• 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.

• Structural Engineering and Mechanics
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• 제67권4호
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• pp.385-390
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• 2018

An incongruity is underlined about the analysis of Timoshenko beams subjected to concentrated loads modelled through the use of generalized functions. While for Euler-Bernoulli beams this modeling always leads to effective results, on the contrary, the contemporary assumptions of concentrated external moment, interpreted as a generalized function (doublet), and of shear deformation determine inconsistent discontinuities in the deflection laws. A physical/theoretical explanation of this not-neglecting incongruity is given in the text.

• International Journal of Aeronautical and Space Sciences
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• 제8권1호
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• pp.140-147
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• 2007

Whenever the hinge axis of aircraft wing rotates, its stiffness varies. Also, there are nonlinearities in the connection of the actuator and the hinge axis, and it is necessary to inspect the coupled effects between the actuator dynamics and the hinge nonlinearity. Nonlinear aeroelastic characteristics are investigated by using the iterative V-g method. Time domain analyses are also performed by using Karpel's minimum state approximation technique. The doublet hybrid method(DHM) is used to calculate the unsteady aerodynamic forces in subsonic regions. Structural nonlinearity located in the load links of the actuator is assumed to be friction. The friction nonlinearity of an actuator is identified by using the describing function technique. The nonlinear flutter analyses have shown that the flutter characteristics significantly depends on the structural nonlinearity as well as the dynamic stiffness of an actuator. Therefore, the dynamic stiffness of an actuator as well as the nonlinear effect of hinge axis are important factors to determine the flutter stability.

• 터널과지하공간
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• 제25권4호
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• pp.320-331
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• 2015

본 논문에서는 독일 북부의 그로스 쉐네벡 지역에서 진행된 EGS 실증프로젝트를 수리자극 시험 중심으로 소개한다. 이 지역에서는 사암 및 화산암으로 이루어진 심도 4 - 4.4 km의 지층 내에 각각 1개의 주입정과 생산정을 갖는 순환 시스템을 구성했다. 정단층 및 주향이동단층 응력상태 하에서 물 또는 젤과 균열지지체를 주입하여 주입정과 생산정에서 각각 수리자극이 이루어졌으며, 그 결과 주입지수가 $0.97m^3/(hr^*MPa)$에서 $7.5m^3/(hr^*MPa)$로 증가하였고 생산성지수는$2.4m^3/(hr^*MPa)$에서 $10.1m^3/(hr^*MPa)$로 4.25배 증가했다. 그러나 주입정과 생산정을 연결하는 순환수리시험에서는 2년간 생산성지수가 $8.9m^3/(hr^*MPa)$에서 $0.6m^3/(hr^*MPa)$까지 감소했다. 화산암층에서의 수리자극에 대해 전단 미끄러짐 해석을 수행한 결과 전단균열의 발생 방향 및 요구되는 유체 압력을 실제 수리자극 결과와 유사하게 예측해 냈다. 화산암층에서의 수리자극 시 미소진동을 관측한 결과 모멘트 규모 -1.8에서 -1.0 범위의 미소진동이 80회 나타나 미소진동의 발생은 극히 미미했다.

• 터널과지하공간
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• 제21권1호
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• pp.11-19
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• 2011

지열에너지는 여러 신재생에너지원 중에서도 기저부하를 담당할 수 있는 중요한 자원으로 인식되고 있다. 국내에서도 천부지열을 이용한 지열냉난방은 효율 높은 신재생에너지 활용 사업으로 그 보급이 활성화 되어 있다. 반면, 전세계적으로 지열 발전 기술이 진일보하고, 그 시장이 크게 확대되고 있는 상황에서 아직까지 국내의 심부 지열을 이용한 지열 발전 기술은 낮은 단계에 머무르고 있다. 이러한 조건에서 2010년 12월에 국내 최초의 EGS(Enhanced Geothermal System) 지열 발전 상용화 기술 개발 과제가 착수되었다. 총 5개년의 기간으로 수행되는 이 과제는 2단계로 구분되어 진행될 계획이다. 처음 2년의 1단계에서는 3 km 심도에서 최소 $100^{\circ}C$의 지열저류층 온도를 확인하는 것을 주요 과제 내용으로 하여 지중 지열수 순환시스템의 설계가 이루어질 예정이다. 이후 3년을 통해 수행될 2단계에서는 5 km 심도의 생산정과 주입정 등 두 개의 지열발전정을 설치하고, 수리자극을 통하여 온도 $180^{\circ}C$의 지열저류층에서 유량 40 kg/s 이상의 지열수를 활용하는 MW급 지열발전소를 건립 운영하게 된다. 이 사업을 성공적으로 추진하기 위하여 현재 지질, 수리지질, 지구물리, 암석역학, 플랜트 엔지니어링 등 다양한 분야의 산학연 연구 기관 등이 망라되어 연구진을 구성한 상태이며, 이후 관심있는 여러 기관과 연구자들의 지원과 참여를 기대하고 있다.