Bibliografías temáticas / Eringen's nonlocal elastica

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Literatura académica sobre el tema "Eringen's nonlocal elastica"

Autor: Grafiati

Publicado: 25 de mayo de 2024

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Artículos de revistas sobre el tema "Eringen's nonlocal elastica"

Jung, Woo-Young, and Sung-Cheon Han. "Nonlocal Elasticity Theory for Transient Analysis of Higher-Order Shear Deformable Nanoscale Plates." Journal of Nanomaterials 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/208393.

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The small scale effect on the transient analysis of nanoscale plates is studied. The elastic theory of the nano-scale plate is reformulated using Eringen’s nonlocal differential constitutive relations and higher-order shear deformation theory (HSDT). The equations of motion of the nonlocal theories are derived for the nano-scale plates. The Eringen’s nonlocal elasticity of Eringen has ability to capture the small scale effects and the higher-order shear deformation theory has ability to capture the quadratic variation of shear strain and consequently shear stress through the plate thickness. The solutions of transient dynamic analysis of nano-scale plate are presented using these theories to illustrate the effect of nonlocal theory on dynamic response of the nano-scale plates. On the basis of those numerical results, the relations between nonlocal and local theory are investigated and discussed, as are the nonlocal parameter, aspect ratio, side-to-thickness ratio, nano-scale plate size, and time step effects on the dynamic response. In order to validate the present solutions, the reference solutions are employed and examined. The results of nano-scale plates using the nonlocal theory can be used as a benchmark test for the transient analysis.

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Ebrahimi, Farzad, and Mohammad Reza Barati. "Electro-magnetic effects on nonlocal dynamic behavior of embedded piezoelectric nanoscale beams." Journal of Intelligent Material Systems and Structures 28, no. 15 (2017): 2007–22. http://dx.doi.org/10.1177/1045389x16682850.

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This article investigates vibration behavior of magneto-electro-elastic functionally graded nanobeams embedded in two-parameter elastic foundation using a third-order parabolic shear deformation beam theory. Material properties of magneto-electro-elastic functionally graded nanobeam are supposed to be variable throughout the thickness based on power-law model. Based on Eringen’s nonlocal elasticity theory which captures the small size effects and using Hamilton’s principle, the nonlocal governing equations of motions are derived and then solved analytically. Then, the influences of elastic foundation, magnetic potential, external electric voltage, nonlocal parameter, power-law index, and slenderness ratio on the frequencies of the embedded magneto-electro-elastic functionally graded nanobeams are studied.

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Mikhasev, G., E. Avdeichik, and D. Prikazchikov. "Free vibrations of nonlocally elastic rods." Mathematics and Mechanics of Solids 24, no. 5 (2018): 1279–93. http://dx.doi.org/10.1177/1081286518785942.

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Several of the Eringen’s nonlocal stress models, including two-phase and purely nonlocal integral models, along with the simplified differential model, are studied in the case of free longitudinal vibrations of a nanorod, for various types of boundary conditions. Assuming the exponential attenuation kernel in the nonlocal integral models, the integro-differential equation corresponding to the two-phase nonlocal model is reduced to a fourth-order differential equation with additional boundary conditions, taking into account nonlocal effects in the neighbourhood of the rod ends. Exact analytical and asymptotic solutions of boundary-value problems are constructed. Formulas for natural frequencies and associated modes found in the framework of the purely nonlocal model and its ‘equivalent’ differential analogue are also compared. A detailed analysis of solutions suggests that the purely nonlocal and differential models lead to ill-posed problems.

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Feo, Luciano, and Rosa Penna. "On Bending of Bernoulli-Euler Nanobeams for Nonlocal Composite Materials." Modelling and Simulation in Engineering 2016 (2016): 1–5. http://dx.doi.org/10.1155/2016/6369029.

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Evaluation of size effects in functionally graded elastic nanobeams is carried out by making recourse to the nonlocal continuum mechanics. The Bernoulli-Euler kinematic assumption and the Eringen nonlocal constitutive law are assumed in the formulation of the elastic equilibrium problem. An innovative methodology, characterized by a lowering in the order of governing differential equation, is adopted in the present manuscript in order to solve the boundary value problem of a nanobeam under flexure. Unlike standard treatments, a second-order differential equation of nonlocal equilibrium elastic is integrated in terms of transverse displacements and equilibrated bending moments. Benchmark examples are developed, thus providing the nonlocality effect in nanocantilever and clampled-simply supported nanobeams for selected values of the Eringen scale parameter.

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Mubasshar, Shahid, and Jaan Lellep. "Natural vibrations of circular nanoarches of piecewise constant thickness." Acta et Commentationes Universitatis Tartuensis de Mathematica 27, no. 2 (2023): 295–318. http://dx.doi.org/10.12697/acutm.2023.27.20.

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The free vibrations of elastic circular arches made of a nano-material are considered. A method of determination of eigenfrequencies of nanoarches weakened with stable cracks is developed making use of the concept of the massless spring and Eringen's nonlocal theory of elasticity. The aim of the paper is to evaluate the sensitivity of eigenfrequencies on the geometrical and physical parameters of the nanoarch.

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Gaygusuzoglu, Guler, Metin Aydogdu, and Ufuk Gul. "Nonlinear Wave Modulation in Nanorods Using Nonlocal Elasticity Theory." International Journal of Nonlinear Sciences and Numerical Simulation 19, no. 7-8 (2018): 709–19. http://dx.doi.org/10.1515/ijnsns-2017-0225.

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AbstractIn this study, nonlinear wave modulation in nanorods is examined on the basis of nonlocal elasticity theory. Eringen's nonlocal elasticity theory is employed to derive nonlinear equations for the motion of nanorods. The analysis of the modulation of axial waves in nonlocal elastic media is performed, and the reductive perturbation method is used for the solution of the nonlinear equations. The propagation of weakly nonlinear and strongly dispersive waves is investigated, and the nonlinear Schrödinger (NLS) equation is acquired as an evolution equation. For the purpose of a numerical investigation of the nonlocal impacts on the NLS equation, it has been investigated whether envelope solitary wave solutions exist by utilizing the physical and geometric features of the carbon nanotubes. Amplitude dependent wave frequencies, phase and group velocities have been obtained and they have compared for the linear local, the linear nonlocal, the nonlinear local and the nonlinear nonlocal cases.

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Shen, Xiao Long, Yong Xin Luo, Lai Xi Zhang, and Hua Long. "Natural Frequency Computation Method of Nonlocal Elastic Beam." Advanced Materials Research 156-157 (October 2010): 1582–85. http://dx.doi.org/10.4028/www.scientific.net/amr.156-157.1582.

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After adopting the constitutive equations of the nonlocal elastic media in the form of Eringen, and making use of the Laplace transformation, the vibration governing equation of nonlocal elastic beam in the Kelvin media are established. Unlike classical elastic models, the stress of a point in a nonlocal model is obtained as a weighted average of the field over the spatial domain, determined by a kernel function based on distance measures. The motion equation of nonlocal elastic beam is an integral differential equation, rather than the differential equation obtained with a classical local model. Solutions for natural frequencies and modes are obtained. Numerical examples demonstrate the efficiency of the proposed method for the beam with simple boundary conditions.

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Xu, S. P., M. R. Xu, and C. M. Wang. "Stability Analysis of Nonlocal Elastic Columns with Initial Imperfection." Mathematical Problems in Engineering 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/341232.

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Investigated herein is the postbuckling behavior of an initially imperfect nonlocal elastic column, which is simply supported at one end and subjected to an axial force at the other movable end. The governing nonlinear differential equation of the axially loaded nonlocal elastic column experiencing large deflection is first established within the framework of Eringen's nonlocal elasticity theory in order to embrace the size effect. Its semianalytical solutions by the virtue of homotopy perturbation method, as well as the successive approximation algorithm, are determined in an explicit form, through which the postbuckling equilibrium loads in terms of the end rotation angle and the deformed configuration of the column at this end rotation are predicted. By comparing the degenerated results with the exact solutions available in the literature, the validity and accuracy of the proposed methods are numerically substantiated. The size effect, as well as the initial imperfection, on the buckled configuration and the postbuckling equilibrium path is also thoroughly discussed through parametric studies.

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Sari, Ma’en S., Mohammad Al-Rbai, and Bashar R. Qawasmeh. "Free vibration characteristics of functionally graded Mindlin nanoplates resting on variable elastic foundations using the nonlocal elasticity theory." Advances in Mechanical Engineering 10, no. 12 (2018): 168781401881345. http://dx.doi.org/10.1177/1687814018813458.

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In this research, free vibration behavior of thick functionally graded nanoplates is carried out using the Chebyshev spectral collocation method. It is assumed that the plates are resting on variable elastic foundations. Eringen’s nonlocal elasticity theory is used to capture the size effect, and Mindlin’s first-order shear deformation plate theory is employed to model the thick nanoplates. Hamilton’s principle along with the differential form of Eringen’s constitutive relations are utilized to obtain the governing partial differential equations of motion for the functionally graded nanoplates under consideration. A numerical solution is presented by applying the spectral collocation method and the natural frequencies are obtained. A parametric study is conducted to study the effects of several factors on the natural frequencies of the functionally graded nanoplates. It is found that the parameters of the variable elastic foundation (Winkler and shear moduli), thickness to length ratio, length to width ratio (aspect ratio), the nonlocal scale coefficient, the gradient index, the foundation type, and the boundary conditions have a remarkable influence on the free vibration characteristics of the functionally graded nanoplates.

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Jung, Woo-Young, and Sung-Cheon Han. "Analysis of Sigmoid Functionally Graded Material (S-FGM) Nanoscale Plates Using the Nonlocal Elasticity Theory." Mathematical Problems in Engineering 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/476131.

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Based on a nonlocal elasticity theory, a model for sigmoid functionally graded material (S-FGM) nanoscale plate with first-order shear deformation is studied. The material properties of S-FGM nanoscale plate are assumed to vary according to sigmoid function (two power law distribution) of the volume fraction of the constituents. Elastic theory of the sigmoid FGM (S-FGM) nanoscale plate is reformulated using the nonlocal differential constitutive relations of Eringen and first-order shear deformation theory. The equations of motion of the nonlocal theories are derived using Hamilton’s principle. The nonlocal elasticity of Eringen has the ability to capture the small scale effect. The solutions of S-FGM nanoscale plate are presented to illustrate the effect of nonlocal theory on bending and vibration response of the S-FGM nanoscale plates. The effects of nonlocal parameters, power law index, aspect ratio, elastic modulus ratio, side-to-thickness ratio, and loading type on bending and vibration response are investigated. Results of the present theory show a good agreement with the reference solutions. These results can be used for evaluating the reliability of size-dependent S-FGM nanoscale plate models developed in the future.

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