• Structural Engineering and Mechanics
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• v.73 no.1
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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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• v.15 no.5
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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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• v.44 no.2
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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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• v.26 no.2
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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.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.4 s.70
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• pp.453-458
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• 2005

This study deals with elasto-plasticity of granular micro-structures which recovers continuum elasto-plasticity in its counterpart. The theory is based on doublet mechanics that assumes particles of finite size and connecting linear springs, and it makes extensions to plasticity. The result shows that the micro model has one to one relationship with the continuum model in the simplest case. Micro-strain and micro-stress of two dimensional plane stress problem were calculated, which shows the behavior of the specimen and verifies the effectiveness of this model.

• Structural Engineering and Mechanics
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• v.67 no.4
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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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• v.8 no.1
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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.

• Tunnel and Underground Space
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• v.25 no.4
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• pp.320-331
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• 2015

This paper presents a case study of an enhanced geothermal system(EGS) demonstration project conducted in $Gro{\ss}$ $Sch{\ddot{o}}nebeck$, Northerm Germany, focusing on hydraulic stimulation. The project was conducted with doublet system in sandstone and volcanic formations at 4 - 4.4 km depth. Under normal faulting to strike-slip faulting stress regime, hydraulic stimulations were conducted at injection and production wells by massive waterfrac and gel-proppant fracturing. Injectivity index increased from $0.97m^3/(hr^*MPa)$ to $7.5m^3/(hr^*MPa)$ and productivity index increased from $2.4m^3/(hr^*MPa)$ to $10.1m^3/(hr^*MPa)$ by a series of hydraulic stimulations at both wells. After circulation tests through injection and production wells, however, productivity index decreased from $8.9m^3/(hr^*MPa)$ to $0.6m^3/(hr^*MPa)$ in two years. Slip tendency analysis for the stimulation in volcanic layer estimated the required pressure for shear slip and its preferred orientations and it showed reasonable match with actual stimulation results. Through the microseismicity observation for the stimulation of volcanic formation, only 80 seismic events with its moment magnitudes in -1.8<$M_W$<-1.0 were observed, which are unexpectedly low for EGS hydraulic stimulation.

• Tunnel and Underground Space
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• v.21 no.1
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• pp.11-19
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• 2011

Geothermal energy is believed to be an important source among the renewable energy sources to provide the base load electricity. Although there has been a drastic increase in the use of geothermal heat pump in Korea, there is no geothermal power plant in operation in Korea. Fortunately, the first EGS (Enhanced Geothermal System) Project in Korea has started in Dec 2010. This five year project is divided into two stages; two years for exploration and drilling of 3 km depth to confirm the minimum target temperature of 100 degrees, and another three years composed drilling 5 km doublet, hydraulic stimulation of geothermal reservoir with expected temperature of 180 degrees (40 kg/s) and construction of MW geothermal power plant in the surface. This EGS project would be a landmark effort that invited a consortium of industry, research institutes and university with expertises in the fields of geology, hydrogeology, geophysics, geomechanics and plant engineering.