• Advances in nano research
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• 제4권4호
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• pp.265-279
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• 2016

Present study interests with the longitudinal forced vibration of nanorods. The nonlocal elasticity theory of Eringen is used in modeling of nanorods. Uniform, linear and sinusoidal axial loads are considered. Dynamic displacements are obtained for nanorods with different geometrical properties, boundary conditions and nonlocal parameters. The nonlocal effect increases dynamic displacement and frequency when compared with local elasticity theory. Present results can be useful for modeling of the axial nanomotors and nanoelectromechanical systems.

• Advances in nano research
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• 제15권1호
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• pp.75-89
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• 2023

In this paper, Bishop theory performs longitudinal vibration analysis of Nano-beams. Its governing equation, due to integrated displacement field and more considered primarily effects compared with other theories, enjoys fully completed status, and more reliable results as well. This article aims to find how Bishop theory and Two-phase elasticity work together. In other words, whether Bishop theory will be compatible with Two-phase local/nonlocal elasticity. Hamilton's principle is employed to derive governing equation of motion, and then the 6th order of Generalized Differential Quadrature Method (GDQM) as a constructive numerical method is utilized to attain the discretized two-phase formulation. To acquire a proper verification procedure, exact solution is prepared to be compared with current results. Furthermore, the effects of key parameters on the objective are investigated.

• Computers and Concrete
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• 제32권2호
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• pp.165-172
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• 2023

The vibration analysis of armchair, zigzag and chiral double-walled carbon nanotubes has been developed by inserting the nonlocal theory of elasticity into thin shell theory. First Donnell shell theory is employed while exercising wave propagation approach. Scale effects are realized by using different values of nonlocal parameters under certain boundary conditions. The natural frequencies have been investigated and displayed for various non-local parameters. It is noticed that on increasing nonlocal parameter, the frequency curve tends to decrease. The frequency estimates of clamped-free boundary condition are less than those of clamped-clamped and simply supported computations. The frequency comparisons are presented for armchair, zigzag and chiral nanotubes. The software MATLAB is used to extract the frequencies of double walled carbon nanotubes.

• Advances in nano research
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• 제14권5호
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• pp.463-474
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• 2023

The purpose of this paper is to present the analysis of propagating and evanescent waves in functionally graded (FG) nanoplates with the consideration of nonlocal effect. The analytical integration nonlocal stress expansion Legendre polynomial method is proposed to obtain complete dispersion curves in the complex domain. Unlike the traditional Legendre polynomial method that expanded the displacement, the presented polynomial method avoids employing the relationship between local stress and nonlocal stress to construct boundary conditions. In addition, the analytical expressions of numerical integrations are presented to improve the computational efficiency. The nonlocal effect, inhomogeneity of medium and their interactions on wave propagation are studied. It is found that the nonlocal effect and inhomogeneity of medium reduce the frequency bandwidth of complex evanescent Lamb waves, and make complex evanescent Lamb waves have a higher phase velocity at low attenuation. The occurrence of intersections of propagating Lamb wave in the nonlocal homogeneous plate needs to satisfy a smaller Poisson's ratio condition than that in the classical elastic theory. In addition, the inhomogeneity of medium enhances the nonlocal effect. The conclusions obtained can be applied to the design and dynamic response evaluation of composite nanostructures.

• Coupled systems mechanics
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• 제9권5호
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• pp.397-410
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• 2020

The present investigation is concerned with two-dimensional deformation in a homogeneous isotropic non local thermoelastic solid with two temperatures due to thermomechanical sources. The theory of memory dependent derivatives has been used for the study. The bounding surface is subjected to concentrated and distributed sources (mechanical and thermal sources). The Laplace and Fourier transforms have been used for obtaining the solution to the problem in the transformed domain. The analytical expressions for displacement components, stress components and conductive temperature are obtained in the transformed domain. For obtaining the results in the physical domain, numerical inversion technique has been applied. Numerical simulated results have been depicted graphically for explaining the effects of nonlocal parameter on the components of displacements, stresses and conductive temperature. Some special cases have also been deduced from the present study. The results obtained in the investigation should be useful for new material designers, researchers and physicists working in the field of nonlocal material sciences.

• Advances in concrete construction
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• 제17권4호
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• pp.187-210
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• 2024

Cantilever structures demonstrate diverse nonlocal effects, resulting in either stiffness hardening or dynamic softening behaviors, as various studies have indicated. This research delves into the free and forced vibration analysis of rotating nanoscale cylindrical beams and tubes under external dynamic stress, aiming to thoroughly explore the nonlocal impact from both angles. Utilizing Euler-Bernoulli and Reddy beam theories, in conjunction with higher-order tube theory and Hamilton's principle, nonlocal governing equations are derived with precise boundary conditions for both local and nonlocal behaviors. The study specifically examines two-dimensional functionally graded materials (2D-FGM), characterized by axially functionally graded (AFG) and radial porosity distributions. The resulting partial differential equations are solved using the generalized differential quadrature element method (GDQEM) and Newmark-beta procedures to acquire time-dependent results. This investigation underscores the significant influence of boundary conditions when nonlocal forces act on cantilever structures.

• 한국초전도ㆍ저온공학회논문지
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• 제25권3호
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• pp.22-27
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• 2023

Magnetic properties of MgB₂ superconducting powder were investigated. M(H), the magnetic field H dependence of magnetization M, was measured and analyzed using a PPMS instrument. The MgB₂ superconducting powder showed high critical current density J_c > ~ 10⁷ A/cm² and clean limit superconducting properties. The equilibrium magnetization M_eq properties of MgB₂ powders exhibiting various superconducting properties were studied. We find that the equilibrium magnetization M_eq(H) properties of MgB₂ powders showing conventional BCS properties deviate from the predictions of the standard local-London theory at temperatures below T = 19 K and are in good agreement with the generalized nonlocal-London theory. Nonlocal-London analysis was used to determine and analyze the nonlocal parameters. The temperature dependence of the London penetration depth values λ(T) was studied.

• Geomechanics and Engineering
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• 제32권2호
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• pp.137-144
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• 2023

The current article studied wave propagation in a nonlocal porous thermoelastic half-space with temperature-dependent properties. The problem is solved in the context of the Green-Lindsay theory (G-L) and the Lord- Shulman theory (L-S) based on thermoelasticity with memory-dependent derivatives. The governing equations of the porous thermoelastic solid are solved using normal mode analysis with an eigenvalue approach. In order to illustrate the analytical developments, the numerical solution is carried out, and the effect of local parameter and temperature-dependent properties on the physical fields are presented graphically.

• 한국산학기술학회논문지
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• 제13권7호
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• pp.3207-3215
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• 2012

본 논문에서는 3차 전단변형이론이 고려된 비국소 탄성 이론을 이용한 나노 판의 휨 및 진동에 대하여 연구하였다. 비국소 탄성 이론은 미소 규모 효과를 고려할 수 있고 3차원 전단변형이론은 나노 판의 두께방향으로의 전단 변형률과 전단응력의 곡선변화 효과를 고려할 수 있다. 이러한 두 가지 이론을 이용하여 나노 판의 처짐과 고유진동수에 미치는 비국소 이론의 효과를 제시하였다. 국소 탄성이론과의 관계를 수치해석 결과를 통하여 고찰하였다. 또한 (i) 비국소 계수, (ii) 나노 판의 적층형태, (iii) 나노 판의 보강 방향 그리고 (iv) 나노 판의 적층 수 등이 나노 판의 무차원 처짐에 미치는 효과에 대하여 관찰하였다. 본 연구의 결과를 검증하기 위해 참고문헌의 결과들과 비교 분석하였으며 해석결과는 참고문헌의 결과들과 잘 일치함을 알 수 있었다. 비국소 이론에 의한 나노 판의 처짐에 관한 연구는 향후 관련연구에 비교자료로 활용될 수 있을 것이다.

• Advances in nano research
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• 제12권2호
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• pp.139-150
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• 2022

This paper presents sets of explicit analytical equations that compute the static displacements of nanobeams by adopting the nonlocal elasticity theory of Eringen within the framework of Euler Bernoulli and Timoshenko beam theories. Castigliano's theorem is applied to an equivalent Virtual Local Beam (VLB) made up of linear elastic material to compute the displacements. The first derivative of the complementary energy of the VLB with respect to a virtual point load provides displacements. The displacements of the VLB are assumed equal to those of the nonlocal beam if nonlocal effects are superposed as additional stress resultants on the VLB. The illustrative equations of displacements are relevant to a few types of loadings combined with a few common boundary conditions. Several equations of displacements, thus derived, matched precisely in similar cases with the equations obtained by other analytical methods found in the literature. Furthermore, magnitudes of maximum displacements are also in excellent agreement with those computed by other numerical methods. These validated the superposition of nonlocal effects on the VLB and the accuracy of the derived equations.