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Journal articles on the topic 'Eringen's nonlocal elastica'

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Published: 25 May 2024

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1

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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2

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 (January 9, 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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3

Mikhasev, G., E. Avdeichik, and D. Prikazchikov. "Free vibrations of nonlocally elastic rods." Mathematics and Mechanics of Solids 24, no. 5 (July 13, 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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4

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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5

Mubasshar, Shahid, and Jaan Lellep. "Natural vibrations of circular nanoarches of piecewise constant thickness." Acta et Commentationes Universitatis Tartuensis de Mathematica 27, no. 2 (December 1, 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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6

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 (December 19, 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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7

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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8

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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9

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 (December 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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10

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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11

Arefi, M., MH Zamani, and M. Kiani. "Size-dependent free vibration analysis of three-layered exponentially graded nanoplate with piezomagnetic face-sheets resting on Pasternak’s foundation." Journal of Intelligent Material Systems and Structures 29, no. 5 (August 1, 2017): 774–86. http://dx.doi.org/10.1177/1045389x17721039.

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This work is devoted to the free vibration nonlocal analysis of an elastic three-layered nanoplate with exponentially graded graphene sheet core and piezomagnetic face-sheets. The rectangular elastic three-layered nanoplate is resting on Pasternak’s foundation. Material properties of the core are supposed to vary along the thickness direction based on the exponential function. The governing equations of motion are derived from Hamilton’s principle based on first-order shear deformation theory. In addition, Eringen’s nonlocal piezo-magneto-elasticity theory is used to consider size effects. The analytical solution is presented to solve seven governing equations of motion using Navier’s solution. Eventually, the natural frequency is scrutinized for different side length ratio, nonlocal parameter, inhomogeneity parameter, and parameters of foundation numerically. The comparison with various references is performed for validation of our analytical results.
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12

Park, Weon-Tae, and Sung-Cheon Han. "Buckling analysis of nano-scale magneto-electro-elastic plates using the nonlocal elasticity theory." Advances in Mechanical Engineering 10, no. 8 (August 2018): 168781401879333. http://dx.doi.org/10.1177/1687814018793335.

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Buckling analysis of nonlocal magneto-electro-elastic nano-plate is investigated based on the higher-order shear deformation theory. The in-plane magnetic and electric fields can be ignored for magneto-electro-elastic nano-plates. According to magneto-electric boundary condition and Maxwell equation, the variation of magnetic and electric potentials along the thickness direction of the magneto-electro-elastic plate is determined. To reformulate the elastic theory of magneto-electro-elastic nano-plate, the nonlocal differential constitutive relations of Eringen is applied. Using the variational principle, the governing equations of the nonlocal theory are derived. The relations between local and nonlocal theories are studied by numerical results. Also, the effects of nonlocal parameters, in-plane load directions, and aspect ratio on buckling response are investigated. Numerical results show the effects of the electric and magnetic potentials. These numerical results can be useful in the design and analysis of advanced structures constructed from magneto-electro-elastic materials.
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13

Arefi, M., M. Kiani, and MH Zamani. "Nonlocal strain gradient theory for the magneto-electro-elastic vibration response of a porous FG-core sandwich nanoplate with piezomagnetic face sheets resting on an elastic foundation." Journal of Sandwich Structures & Materials 22, no. 7 (August 20, 2018): 2157–85. http://dx.doi.org/10.1177/1099636218795378.

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The free vibration analysis of a nonlocal strain gradient elastic sandwich nanoplate with porous graded core and piezomagnetic face sheets is presented in this paper. The rectangular elastic sandwich nanoplate is resting on Pasternak's foundation. Porosities are distributed evenly and unevenly through the thickness of the core. The gradation of material properties having porosities is described using a modified power-law function. A nonlocal parameter and a strain gradient parameter are employed to describe both stiffness reduction and stiffness enhancement of nanoplates. The governing equations of the motion are derived from Hamilton’s principle based on the first order shear deformation theory. In addition, Eringen’s nonlocal strain gradient piezo-magneto-elasticity theory is used to consider nanoscale effects. The analytical solution is presented to solve seven governing equations of motion using Navier’s solution. Eventually, the natural frequency is surveyed for different side length ratios, nonlocal coefficient, porosity volume fraction, and parameters of foundation numerically with even and uneven porosity distributions.
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14

Selvamani, Rajendran, M. Mahaveer Sree Jayan, Rossana Dimitri, Francesco Tornabene, and Farzad Ebrahimi. "Nonlinear magneto-thermo-elastic vibration of mass sensor armchair carbon nanotube resting on an elastic substrate." Curved and Layered Structures 7, no. 1 (October 7, 2020): 153–65. http://dx.doi.org/10.1515/cls-2020-0012.

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AbstractThe present paper aims at studying the nonlinear ultrasonic waves in a magneto-thermo-elastic armchair single-walled (SW) carbon nanotube (CNT) with mass sensors resting on a polymer substrate. The analytical formulation accounts for small scale effects based on the Eringen’s nonlocal elasticity theory. The mathematical model and its differential equations are solved theoretically in terms of dimensionless frequencies while assuming a nonlinear Winkler-Pasternak-type foundation. The solution is obtained by means of ultrasonic wave dispersion relations. A parametric work is carried out to check for the effect of the nonlocal scaling parameter, together with the magneto-mechanical loadings, the foundation parameters, the attached mass, boundary conditions and geometries, on the dimensionless frequency of nanotubes. The sensitivity of the mechanical response of nanotubes investigated herein, could be of great interest for design purposes in nano-engineering systems and devices.
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15

Arani, Ali Ghorbanpour, and Reza Kolahchi. "Nonlinear vibration and instability of embedded double-walled carbon nanocones based on nonlocal Timoshenko beam theory." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 228, no. 4 (May 17, 2013): 690–702. http://dx.doi.org/10.1177/0954406213490128.

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Nonlinear vibration and instability of embedded double-walled carbon nanocones subjected to axial load are investigated in this article based on Eringen's nonlocal theory and Timoshenko beam model. The elastic medium is simulated as Pasternak foundation and the van der Waals forces between the inner and the outer layers of double-walled carbon nanocones are taken into account. Using von Kármán geometric nonlinearity, energy method and Hamilton’s principle, the nonlocal nonlinear motion equations are obtained. The differential quadrature method is applied to discretize the motion equations, which are then solved to obtain the nonlinear frequency and critical fluid velocity of viscous-fluid-conveying double-walled carbon nanocones. A detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, thickness-to-length ratio, temperature change, apex angles, elastic medium and van der Waals forces on the dimensionless frequency and critical buckling load of double-walled carbon nanocones. The results show that the small-size effect on the nonlinear frequency is significant and cannot be neglected; also, the nonlinear frequency and critical buckling load decrease with increasing the cone apex-angle.
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16

Ebrahimi, F., and M. R. Barati. "Buckling Analysis of Smart Size-Dependent Higher Order Magneto-Electro-Thermo-Elastic Functionally Graded Nanosize Beams." Journal of Mechanics 33, no. 1 (May 24, 2016): 23–33. http://dx.doi.org/10.1017/jmech.2016.46.

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AbstractThe present paper examines the thermal buckling of nonlocal magneto-electro-thermo-elastic functionally graded (METE-FG) beams under various types of thermal loading namely uniform, linear and sinusoidal temperature rise and also heat conduction. The material properties of nanobeam are graded in the thickness direction according to the power-law distribution. Based on a higher order beam theory as well as Hamilton's principle, nonlocal governing equations for METE-FG nanobeam are derived and are solved using Navier type method. The small size effect is captured using Eringen's nonlocal elasticity theory. The most beneficial feature of the present beam model is to provide a parabolic variation of the transverse shear strains across the thickness direction and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. Various numerical examples are presented investigating the influences of thermo-mechanical loadings, magnetic potential, external electric voltage, power-law index, nonlocal parameter and slenderness ratio on thermal buckling behavior of nanobeams made of METE-FG materials.
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17

Wu, Chih-Ping, and Jyun-Yu Liou. "RMVT-Based Nonlocal Timoshenko Beam Theory for Stability Analysis of Embedded Single-Walled Carbon Nanotube with Various Boundary Conditions." International Journal of Structural Stability and Dynamics 16, no. 10 (December 2016): 1550068. http://dx.doi.org/10.1142/s0219455415500686.

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On the basis of Reissner’s mixed variational theorem (RMVT), a nonlocal Timoshenko beam theory (TBT) is developed for the stability analysis of a single-walled carbon nanotube (SWCNT) embedded in an elastic medium, with various boundary conditions and under axial loads. Eringen’s nonlocal elasticity theory is used to account for the small length scale effect. The strong formulations of the RMVT-based nonlocal TBT and its associated possible boundary conditions are presented. The interaction between the SWCNT and its surrounding elastic medium is simulated using the Pasternak foundation models. The critical load parameters of the embedded SWCNT with different boundary conditions are obtained by using the differential quadrature (DQ) method, in which the locations of [Formula: see text] sampling nodes are selected as the roots of [Formula: see text]-order Chebyshev polynomials. The results of the RMVT-based nonlocal TBT are compared with those obtained using the principle of virtual displacement (PVD)-based nonlocal TBT available in the literature. The influences of some crucial effects on the critical load parameters of the embedded SWCNT are examined, such as different boundary conditions, Winkler stiffness and shear modulus of the foundation, aspect ratios, and the nonlocal parameter.
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18

Mirzade, F. Kh. "Small-Scale Effect on Longitudinal Wave Propagation in Laser-Excited Plates." Journal of Nanoscience 2014 (October 21, 2014): 1–8. http://dx.doi.org/10.1155/2014/513010.

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Longitudinal wave propagation in an elastic isotopic laser-excited solid plate with atomic defect (vacancies, interstitials) generation is studied by the nonlocal continuum model. The nonlocal differential constitutive equations of Eringen are used in the formulations. The coupled governing equations for the dynamic of elastic displacement and atomic defect concentration fields are obtained. The frequency equations for the symmetrical and antisymmetrical motions of the plate are found and discussed. Explicit expressions for different characteristics of waves like phase velocity and attenuation (amplification) coefficients are derived. It is shown that coupling between the displacement and defect concentration fields affects the wave dispersion characteristics in the nonlocal elasticity. The dispersion curves of the elastic-diffusion instability are investigated for different pump parameters and larger wave numbers.
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19

Strozzi, Matteo, Isaac E. Elishakoff, Michele Bochicchio, Marco Cocconcelli, Riccardo Rubini, and Enrico Radi. "Nonlocal-Strain-Gradient-Based Anisotropic Elastic Shell Model for Vibrational Analysis of Single-Walled Carbon Nanotubes." C 10, no. 1 (March 7, 2024): 24. http://dx.doi.org/10.3390/c10010024.

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In this study, a new anisotropic elastic shell model with a nonlocal strain gradient is developed to investigate the vibrations of simply supported single-walled carbon nanotubes (SWCNTs). The Sanders–Koiter shell theory is used to obtain strain–displacement relationships. Eringen’s nonlocal elasticity and Mindlin’s strain gradient theories are adopted to derive the constitutive equations, where the anisotropic elasticity constants are expressed via Chang’s molecular mechanics model. An analytical method is used to solve the equations of motion and to obtain the natural frequencies of SWCNTs. First, the anisotropic elastic shell model without size effects is validated through comparison with the results of molecular dynamics simulations reported in the literature. Then, the effects of the nonlocal and material parameters on the natural frequencies of SWCNTs with different geometries and wavenumbers are analyzed. From the numerical simulations, it is confirmed that the natural frequencies decrease as the nonlocal parameter increases, while they increase as the material parameter increases. As new results, the reduction in natural frequencies with increasing SWCNT radius and the increase in natural frequencies with increasing wavenumber are both amplified as the material parameter increases, while they are both attenuated as the nonlocal parameter increases.
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20

Ebrahimi, Farzad, and Mohammad Reza Barati. "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment." Journal of Vibration and Control 24, no. 3 (April 29, 2016): 549–64. http://dx.doi.org/10.1177/1077546316646239.

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In this paper, vibration characteristics of magneto-electro-thermo-elastic functionally graded (METE-FG) nanobeams is investigated in the framework of third order shear deformation theory. Magneto-electro-thermo-elastic properties of FG nanobeam are supposed to vary smoothly and continuously along the thickness based on power-law form. To capture the small size effects, Eringen’s nonlocal elasticity theory is adopted. By using the Hamilton’s principle, the nonlocal governing equations are derived and then solved analytically to obtain the natural frequencies of METE-FG nanobeams. The reliability of proposed model and analytical method in predicting natural frequencies of METE-FG nanobeam is evaluated with comparison to some cases in the literature. Numerical results are provided indicating the influences of several parameters including magnetic potential, external electric voltage, temperature fields, power-law exponent, nonlocal parameter and slenderness ratio on the frequencies of METE-FG nanobeams. It is found that the vibrational behavior of METE-FG nanobeams is significantly impressed by these effects.
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21

Abdollahi, F., and A. Ghassemi. "Surface and Nonlocal Effects on Coupled In-Plane Shear Buckling and Vibration of Single-Layered Graphene Sheets Resting on Elastic Media and Thermal Environments using DQM." Journal of Mechanics 34, no. 6 (May 10, 2018): 847–62. http://dx.doi.org/10.1017/jmech.2018.14.

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AbstractIn this article, surface and nonlocal effects are explored in the analysis of buckling and vibration in rectangular single-layered graphene sheets embedded in elastic media and subjected to coupled in-plane loadings and thermal conditions. The small-scale and surface effects are taken into account using the Eringen's nonlocal elasticity and Gurtin-Murdoch's theory, respectively. Using the principle of virtual work, the governing equations considering small-scale are derived for the nanoplate bulk and surface. The differential quadrature method (DQM) is utilized for the solution of the relevant problems and the results are validated against Navier's solutions. The impacts of the nonlocal parameter, Winkler and shear elastic moduli, temperature rise, boundary conditions, and the in-plane biaxial, uniaxial, and shear loadings on the surface effects of buckling and vibration are investigated. Numerical results show that increasing nonlocal parameter leads to enhanced surface effects on both buckling and vibration. This is in contrast to those reported elsewhere. Moreover, increasing in-plane loads are observed to enhance surface effects on vibration. On the other hand, the nonlocal parameter is observed to have more pronounced effects on shear buckling and vibration of plates subjected to coupled in-plane shear loads than those subjected to biaxial and uniaxial loads. This is while surface effects have greater impacts on biaxial buckling and vibration of nanoplates than on shear buckling and vibration.
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22

Nalbant, Mustafa Oguz, Süleyman Murat Bağdatli, and Ayla Tekin. "Investigation of Free Vibrations of Stepped Nanobeam Embedded In Elastic Foundation." International Conference on Applied Engineering and Natural Sciences 1, no. 1 (July 21, 2023): 445–52. http://dx.doi.org/10.59287/icaens.1037.

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The free vibration of stepped nanobeams embedded in the elastic foundation was investigated using Eringen's nonlocal elasticity theory. It is fixed at the system ends with a simple-simple support. The stepped nanbeam’s equations of motion are obtained by using Hamilton's principle. Multi-time scale, which is the perturbation methods, was used for the analytical solution of the equations. To observe the effects of nano size effect, elastic basis coefficient and step location, natural frequencies of the first three modes of the system were obtained for different non-local parameter values, elastic foundation coefficients, step rates and step positions. In the results, it was seen that the non-local parameter had a negative effect on the natural frequency. The elastic foundation coefficient has been shown to reduce vibration amplitudes.
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23

De Rosa, Maria Anna, Isaac Elishakoff, Antonella Onorato, and Maria Lippiello. "Dynamic Analysis of a Timoshenko–Ehrenfest Single-Walled Carbon Nanotube in the Presence of Surface Effects: The Truncated Theory." Applied Mechanics 4, no. 4 (October 19, 2023): 1100–1113. http://dx.doi.org/10.3390/applmech4040056.

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The main objective of this paper is to study the free vibration of a Timoshenko–Ehrenfest single-walled carbon nanotube based on the nonlocal theory and taking surface effects into account. To model these effects on frequency response of nanotubes, we use Eringen’s nonlocal elastic theory and surface elastic theory proposed by Gurtin and Murdoch to modify the governing equation. A modified version of Timoshenko nonlocal elasticity theory—known as the nonlocal truncated Timoshenko beam theory—is put forth to investigate the free vibration behavior of single-walled carbon nanotubes (SWCNTs). Using Hamilton’s principle, the governing equations and the corresponding boundary conditions are derived. Finally, to check the accuracy and validity of the proposed method, some numerical examples are carried out. The impacts of the nonlocal coefficient, surface effects, and nanotube length on the free vibration of single-walled carbon nanotubes (SWCNTs) are evaluated, and the results are compared with those found in the literature. The findings indicate that the length of the nanotube, the nonlocal parameter, and the surface effect all play important roles and should not be disregarded in the vibrational analysis of nanotubes. Finally, the results show how effective and successful the current formulation is at explaining the behavior of nanobeams.
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24

Yayli, Mustafa Ö., Suheyla Y. Kandemir, and Ali E. Çerçevik. "Torsional vibration of cracked carbon nanotubes with torsional restraints using Eringen’s nonlocal differential model." Journal of Low Frequency Noise, Vibration and Active Control 38, no. 1 (December 26, 2018): 70–87. http://dx.doi.org/10.1177/1461348418813255.

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Free torsional vibration of cracked carbon nanotubes with elastic torsional boundary conditions is studied. Eringen’s nonlocal elasticity theory is used in the analysis. Two similar rotation functions are represented by two Fourier sine series. A coefficient matrix including torsional springs and crack parameter is derived by using Stokes’ transformation and nonlocal boundary conditions. This useful coefficient matrix can be used to obtain the torsional vibration frequencies of cracked nanotubes with restrained boundary conditions. Free torsional vibration frequencies are calculated by using Fourier sine series and compared with the finite element method and analytical solutions available in the literature. The effects of various parameters such as crack parameter, geometry of nanotubes, and deformable boundary conditions are discussed in detail.
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25

Sayyad, Atteshamuddin S., and Yuwaraj M. Ghugal. "Bending, Buckling and Free Vibration Analysis of Size-Dependent Nanoscale FG Beams Using Refined Models and Eringen’s Nonlocal Theory." International Journal of Applied Mechanics 12, no. 01 (January 2020): 2050007. http://dx.doi.org/10.1142/s1758825120500076.

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In this study, a theoretical unification of twenty-one nonlocal beam theories are presented by using a unified nonlocal beam theory. The small-scale effect is considered based on the nonlocal differential constitutive relations of Eringen. The present unified theory satisfies traction free boundary conditions at the top and bottom surface of the nanobeam and hence avoids the need of shearing correction factor. Hamilton’s principle is employed to derive the equations of motion. The present unified nonlocal formulation is applied for the bending, buckling and free vibration analysis of functionally graded (FG) nanobeams. The elastic properties of FG material vary continuously by gradually changing the volume fraction of the constituent materials in the thickness direction. Closed-form analytical solutions are obtained by using Navier’s solution technique. Non-dimensional displacements, stresses, natural frequencies and critical buckling loads for FG nanobeams are presented. The numerical results presented in this study can be served as a benchmark for future research.
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26

Fuschi, P., and A. A. Pisano. "Symmetric Structures Made of a Nonlocal Elastic Material." International Journal of Applied Mechanics 08, no. 04 (June 2016): 1650052. http://dx.doi.org/10.1142/s1758825116500526.

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The paper focuses on the analysis of symmetric structures in the context of nonlocal integral elasticity of Eringen-type. In particular, it highlights how the standard (local-type) concept of structural symmetry cannot be applied in a straightforward manner, but it has to be redefined involving an enlarged symmetric model of the structure. Such enlarged model is indeed able to take into account the nonlocal effects exerted on the (standard) symmetric portion of the structure chosen for the analysis by the portion neglected. The appropriate boundary conditions that have to be applied to the enlarged symmetric model for guaranteeing the exact matching between the mirrored symmetric solution and the complete one, are also discussed. Two numerical examples are solved by means of a nonlocal version of the finite element method and the results obtained are critically discussed.
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27

Ghannadpour, Seyyed Amir Mahdi, and Bijan Mohammadi. "Buckling Analysis of Micro- and Nano-Rods/Tubes Based on Nonlocal Timoshenko Beam Theory Using Chebyshev Polynomials." Advanced Materials Research 123-125 (August 2010): 619–22. http://dx.doi.org/10.4028/www.scientific.net/amr.123-125.619.

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This paper presents the elastic buckling behavior of nonlocal micro- and nano- Timoshenko rods/tubes based on Eringen’s nonlocal elasticity theory. The critical buckling loads are obtained using the theorem of minimum total potential energy and Chebyshev polynomial functions. The present method, which uses Rayleigh–Ritz technique in this paper, provides an efficient and extremely accurate buckling solution. Numerical results for a variety of some micro- and nano-rods/tubes with various boundary conditions are given and compared with the available results wherever possible. Through the comparison of the results and the appropriate discussion, the knowledge of the level of capability of the developed method is promoted. The small scale effects on the buckling loads of rods/tubes are determined and discussed.
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Khosravi, Farshad, Seyyed Amirhosein Hosseini, and Hamid Norouzi. "Exponential and harmonic forced torsional vibration of single-walled carbon nanotube in an elastic medium." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234, no. 10 (February 6, 2020): 1928–42. http://dx.doi.org/10.1177/0954406220903341.

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In this study, free torsional vibration and forced torsional vibration analysis under the time-dependent exponential and harmonic torsional loadings in single-walled carbon nanotube are investigated. The SWCNT is embedded in an elastic medium. Eringen's theory among the small-scale theories is selected. The nonlocal differential constitutive relation and corresponding boundary condition are derived via Hamilton's principle. Clamped–clamped boundary condition is utilized. The assumed modes method is employed for the dynamic torsional vibration in order to discretize the derived governing equations. The novelty of this work is devoted to the analysis of forced torsional vibration of a carbon nanotube embedded in an elastic medium under the various loadings. The angular displacement for the resonance frequency neglecting the elastic medium is illustrated. For the free analysis, the first three nondimensional natural frequencies with various small-scale parameters and stiffness of the elastic medium are calculated. The results are compared with another study for the first 10 mode numbers. The effects of the nonlocal parameter, length of carbon nanotube, stiffness of the elastic medium, thickness, time constant, and excitation frequency on the nondimensional and dimensional angular displacements are investigated, dynamically. For the greater values of the stiffness of the medium, the nonlocal parameter becomes negligible. When a time-dependent exponential torque is applied to the model, the angular displacement becomes greater and then lower by an increase in the value of the length, but the nondimensional angular displacement decreases continuously by increasing the value of the length under the time-dependent harmonic loading. Moreover, the angular displacement for a determined time becomes lower first and then becomes greater by increasing the time constant.
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29

Wu, Chih-Ping, and Yen-Jung Chen. "Cylindrical Bending Vibration of Multiple Graphene Sheet Systems Embedded in an Elastic Medium." International Journal of Structural Stability and Dynamics 19, no. 04 (April 2019): 1950035. http://dx.doi.org/10.1142/s0219455419500354.

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Based on the Eringen nonlocal elasticity theory and multiple time scale method, an asymptotic nonlocal elasticity theory is developed for cylindrical bending vibration analysis of simply-supported, [Formula: see text]-layered, and uniformly or nonuniformly-spaced, graphene sheet (GS) systems embedded in an elastic medium. Both the interactions between the top and bottom GSs and their surrounding medium and the interactions between each pair of adjacent GSs are modeled as one-parameter Winkler models with different stiffness coefficients. In the formulation, the small length scale effect is introduced to the nonlocal constitutive equations by using a nonlocal parameter. The nondimensionalization, asymptotic expansion, and successive integration mathematical processes are performed for a typical GS. After assembling the motion equations for each individual GS to form those of the multiple GS system, recurrent sets of motion equations can be obtained for various order problems. Nonlocal multiple classical plate theory (CPT) is derived as a first-order approximation of the current nonlocal plane strain problem, and the motion equations for higher-order problems retain the same differential operators as those of nonlocal multiple CPT, although with different nonhomogeneous terms. Some nonlocal plane strain solutions for the natural frequency parameters of the multiple GS system with and without being embedded in the elastic medium and their corresponding mode shapes are presented to demonstrate the performance of the asymptotic nonlocal elasticity theory.
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30

Khosravi, Farshad, Seyyed Amirhosein Hosseini, and Abdelouahed Tounsi. "Forced Axial Vibration of a Single-Walled Carbon Nanotube Embedded in Elastic Medium under Various Moving Forces." Journal of Nano Research 63 (June 2020): 112–33. http://dx.doi.org/10.4028/www.scientific.net/jnanor.63.112.

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The dynamic free and forced axial vibrations subjected to moving exponential and harmonic axial forces of a single-walled carbon nanotube (SWCNT) embedded in an elastic medium, are studied in this paper. Two different boundary conditions of SWCNT, including clamped-clamped and clamped-free, are taken into account. Eringen’s nonlocal elasticity theory is used to show the nonlocality for the model. The constitutive equations and their boundary conditions are derived by Hamilton’s principle. Employing the general solution, the derived equations are analytically solved to obtain two items. Firstly, the axial natural frequencies, secondly, the time-domain axial displacements at the middle of the carbon nanotube (CNT), and then the maximum axial displacements. The responses are validated with previous works, and the results demonstrates good agreement to them to verify the influence of the nonlocal parameter on the nondimensional natural frequencies for three various mode numbers. In the time-domain section, the effects of the nonlocal parameter, length, nondimensional stiffness of the elastic medium, and velocity of the moving load on the axial displacement are investigated. Also, the influences of the excitation frequency to natural frequency for the harmonic moving load, as well as the time constant for the exponential moving load on the axial displacement, are illustrated. Finally, the effect of the nonlocal parameter on the maximum axial deflection versus velocity parameter is schematically indicated.
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31

Dehghan, M., F. Ebrahimi, and M. Vinyas. "Wave dispersion analysis of magnetic-electrically affected fluid-conveying nanotubes in thermal environment." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 19-20 (August 27, 2019): 7116–31. http://dx.doi.org/10.1177/0954406219869752.

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In this paper, the wave propagation analysis of fluid-conveying Magneto-Electro-Elastic (MEE) nanotube subjected to multi-physical fields is investigated via nonlocal strain gradient elasticity theory (NSGT). To take into account the small-scale effects, the nonlocal elasticity theory of Eringen is employed. Nonlocal governing equations of MEE nanotube have been derived utilizing Hamilton’s principle. The results of this study have been verified by checking them of antecedent investigations. An analytical solution of governing equations is used to acquire wave frequencies and phase velocities. The Knudsen number is considered to study the slip boundary wall of nanotube and flow. The effects of various parameters such as multi-physical fields, the Knudsen number, different mode, length parameter, nonlocal parameter, fluid velocity, fluid effect and the slip boundary condition on wave propagation characteristics of fluid-conveying MEE nanotube are investigated in detail.
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32

Chakraverty, Snehashish, and Subrat Kumar Jena. "Free Vibration of Single Walled Carbon Nanotube Resting on Exponentially Varying Elastic Foundation." Curved and Layered Structures 5, no. 1 (November 1, 2018): 260–72. http://dx.doi.org/10.1515/cls-2018-0019.

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Abstract In this article, free vibration of SingleWalled Carbon Nanotube (SWCNT) resting on exponentially varying Winkler elastic foundation is investigated by using Differential Quadrature Method (DQM). Euler-Bernoulli beam theory is considered in conjunction with the nonlocal elasticity theory of Eringen. Step by step procedure is included and MATLAB code has been developed to obtain the numerical results for different scaling parameters as well as for four types of edge conditions. Obtained results are validated with known results in special cases showing good agreement. Further, numerical as well as graphical results are illustrated to show the effects of nonuniform parameter, nonlocal parameter, aspect ratio,Winkler modulus parameter and edge conditions on the frequency parameters.
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33

Ebrahimi, Farzad, and Mohammad Reza Barati. "Vibration analysis of embedded biaxially loaded magneto-electrically actuated inhomogeneous nanoscale plates." Journal of Vibration and Control 24, no. 16 (May 11, 2017): 3587–607. http://dx.doi.org/10.1177/1077546317708105.

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In this research, a free vibration study of a biaxially compressed magneto-electro-elastic functionally graded (MEE-FG) nanoplate resting on an elastic substrate is carried out according to a trigonometric plate formulation. Spatially graded MEE properties of the nanoplate are described according to a power-law distribution. Eringen’s nonlocal elasticity model is utilized to incorporate the small-scale influences. The distributions of magneto-electrical potentials in the thickness direction are considered as a combination of cosine and linear variations. The governing equations of the present plate model are obtained employing Hamilton’s principle. Some admissible functions are introduced to satisfy different boundary conditions and solving these equations. It is indicated that vibration frequencies of the MEE-FG nanoplate are dramatically affected by biaxial compression, magnetic potential, electric voltage, elastic substrate, small-scale parameter, and material gradation.
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34

Abouelregal, Ahmed E., and Marin Marin. "The Size-Dependent Thermoelastic Vibrations of Nanobeams Subjected to Harmonic Excitation and Rectified Sine Wave Heating." Mathematics 8, no. 7 (July 10, 2020): 1128. http://dx.doi.org/10.3390/math8071128.

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In this article, a nonlocal thermoelastic model that illustrates the vibrations of nanobeams is introduced. Based on the nonlocal elasticity theory proposed by Eringen and generalized thermoelasticity, the equations that govern the nonlocal nanobeams are derived. The structure of the nanobeam is under a harmonic external force and temperature change in the form of rectified sine wave heating. The nonlocal model includes the nonlocal parameter (length-scale) that can have the effect of the small-scale. Utilizing the technique of Laplace transform, the analytical expressions for the studied fields are reached. The effects of angular frequency and nonlocal parameters, as well as the external excitation on the response of the nanobeam are carefully examined. It is found that length-scale and external force have significant effects on the variation of the distributions of the physical variables. Some of the obtained numerical results are compared with the known literature, in which they are well proven. It is hoped that the obtained results will be valuable in micro/nano electro-mechanical systems, especially in the manufacture and design of actuators and electro-elastic sensors.
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35

Ebrahimi, Farzad, and Mohammad Reza Barati. "Modeling of smart magnetically affected flexoelectric/piezoelectric nanostructures incorporating surface effects." Nanomaterials and Nanotechnology 7 (January 1, 2017): 184798041771310. http://dx.doi.org/10.1177/1847980417713106.

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In this article, electromechanical buckling behavior of size-dependent flexoelectric/piezoelectric nanobeams is investigated based on nonlocal and surface elasticity theories. Flexoelectricity represents the coupling between the strain gradients and electrical polarizations. Flexoelectric/piezoelectric nanostructures can tolerate higher buckling loads compared with conventional piezoelectric ones, especially at lower thicknesses. Nonlocal elasticity theory of Eringen is applied for analyzing flexoelectric/piezoelectric nanobeams for the first time. The flexoelectric/piezoelectric nanobeams are assumed to be in contact with a two-parameter elastic foundation which consists of infinite linear springs and a shear layer. The residual surface stresses which are usually neglected in modeling of flexoelectric nanobeams are incorporated into nonlocal elasticity to provide better understanding of the physics of the problem. Applying an analytical method which satisfies various boundary conditions, the governing equations obtained from Hamilton’s principle are solved. The reliability of the present approach is verified by comparing the obtained results with those provided in literature. Finally, the influences of nonlocal parameter, surface effects plate geometrical parameters, elastic foundation, and boundary conditions on the buckling characteristics of the flexoelectric/piezoelectric nanobeams are explored in detail.
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36

Zenkour, Ashraf M., Mashhour A. Alazwari, and Ahmed F. Radwan. "A Quasi-3D Higher-Order Theory for Bending of FG Nanoplates Embedded in an Elastic Medium in a Thermal Environment." Mathematics 10, no. 2 (January 13, 2022): 234. http://dx.doi.org/10.3390/math10020234.

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This paper presents the effects of temperature and the nonlocal coefficient on the bending response of functionally graded (FG) nanoplates embedded in an elastic foundation in a thermal environment. The effects of transverse normal strain, as well as transverse shear strains, are considered where the variation of the material properties of the FG nanoplate are considered only in thickness direction. Unlike other shear and deformations theories in which the number of unknown functions is five and more, the present work uses shear and deformations theory with only four unknown functions. The four-unknown normal and shear deformations model, associated with Eringen nonlocal elasticity theory, is used to derive the equations of equilibrium utilizing the principle of virtual displacements. The effects due to nonlocal coefficient, side-to-thickness ratio, aspect ratio, normal and shear deformations, thermal load and elastic foundation parameters, as well as the gradation in FG nanoplate bending, are investigated. In addition, for validation, the results obtained from the present work are compared to ones available in the literature.
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37

Wang, C. M., H. Zhang, R. P. Gao, W. H. Duan, and N. Challamel. "Hencky Bar-Chain Model for Buckling and Vibration of Beams with Elastic End Restraints." International Journal of Structural Stability and Dynamics 15, no. 07 (August 31, 2015): 1540007. http://dx.doi.org/10.1142/s0219455415400076.

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This paper presents the Hencky bar-chain model (HBM) for buckling and vibration analyses of Euler–Bernoulli beams with elastic end restraints. The Hencky bar-chain comprises rigid beam segments (of length a = L/n where L is the total length of beam and n the number of beam segments) connected by frictionless hinges with elastic rotational springs of stiffness EI/a where EI is the flexural rigidity of the beam. The elasticity and the mass of the beam are concentrated at the hinges with rotational springs. The key contribution of this paper lies in the modeling of the elastic end restraints of the Hencky bar-chain that will simulate the same buckling and vibration results as that furnished by the first-order central finite difference beam model (FDM) which was earlier shown to be analogous to the HBM. The establishment of such a physical discrete beam model allows one to obtain solutions for beam-like structure with repetitive cells (or elements) as well as to calibrate the Eringen's coefficient e0 in the nonlocal beam theory that captures the small length scale effect.
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38

Vosoughi, AR, and MR Nikoo. "A new mixed method for nonlinear fuzzy free vibration analysis of nanobeams on nonlinear elastic foundation." Journal of Vibration and Control 24, no. 24 (May 16, 2016): 5765–73. http://dx.doi.org/10.1177/1077546316648491.

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A new mixed method for nonlinear fuzzy free vibration analysis of nanobeams on nonlinear elastic foundation is introduced. The governing equations are derived based on the first-order shear deformation theory (FSDT) in conjunction with the von-Kármán’s assumptions and the Eringen’s nonlocal elasticity theory. The differential quadrature method (DQM) is employed to discretize the governing equations and the related boundary conditions. The direct displacement control iterative method is used to solve the discretized system of equations. The fuzzy transformation method (FTM) is coupled with the solution to incorporate effects of different uncertainties such as the small scale effect parameter, nonlinear elastic foundation parameters and vibration amplitude of the nanobeam. Applicability, rapid rate of convergence and high accuracy of the presented method are shown and significant effects of the nonlinearity on the response of nanobeams are investigated via solving some examples.
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39

Kadari, Belkacem, Aicha Bessaim, Abdelouahed Tounsi, Houari Heireche, Abdelmoumen Anis Bousahla, and Mohammed Sid Ahmed Houari. "Buckling Analysis of Orthotropic Nanoscale Plates Resting on Elastic Foundations." Journal of Nano Research 55 (November 2018): 42–56. http://dx.doi.org/10.4028/www.scientific.net/jnanor.55.42.

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This work presents the buckling investigation of embedded orthotropic nanoplates by using a new hyperbolic plate theory and nonlocal small-scale effects. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modeled with only three unknowns and three governing equation as the case of the classical plate theory (CPT) and which is even less than the first order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Nonlocal differential constitutive relations of Eringen is employed to investigate effects of small scale on buckling of the rectangular nanoplate. The elastic foundation is modeled as two-parameter Pasternak foundation. The equations of motion of the nonlocal theories are derived and solved via Navier's procedure for all edges simply supported boundary conditions. The proposed theory is compared with other plate theories. Analytical solutions for buckling loads are obtained for single-layered graphene sheets with isotropic and orthotropic properties. The results presented in this study may provide useful guidance for design of orthotropic graphene based nanodevices that make use of the buckling properties of orthotropic nanoplates. Verification studies show that the proposed theory is not only accurate and simple in solving the buckling nanoplates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns. Keywords: Buckling; orthotropic nanoplates; a simple 3-unknown theory; nonlocal elasticity theory; Pasternak’s foundations. * Corresponding author; Email-tou_abdel@yahoo.com
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40

Arani, A. Ghorbanpour, AA Shirali, M. Noudeh Farahani, S. Amir, and A. Loghman. "Nonlinear vibration analysis of protein microtubules in cytosol conveying fluid based on nonlocal elasticity theory using differential quadrature method." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 1 (April 19, 2012): 137–45. http://dx.doi.org/10.1177/0954406212445151.

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In this article, nonlinear vibration of protein microtubules in cytosol with internal flow is studied. Based on the Euler–Bernoulli beam theory with von Kármán nonlinearity type and using Hamilton’s principle, the equations of motion for fluid-conveying microtubules are derived. The size effect is taken into account using Eringen’s nonlocal elasticity theory; moreover, the effect of an elastic surrounding filament network and the surface traction of cytosol are studied. The governing differential equations for vibration response of microtubules are solved using the differential quadrature method. The nonlinear frequency response of microtubules, considering the effect of microtubule properties, size effect, the surrounding elastic media, and the fluid motion are reported in this article. It has been found that the effect of nonlocal parameter on the vibration behavior and instability of the embedded microtubule conveying fluid are significant. In this regard, we need to point out that the critical flow velocity for a range of nonlocality parameter from 0 to 2 nm varies between 41 and 47 m/s, which should be avoided due to instability of the microtubule system. Therefore, they should be taken into account in the design of nano/micro-devices for measuring density of a fluid, such as drugs flowing through such microtubules, with great applications in biomechanics.
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41

Abouelregal, Ahmed E., and Hamid M. Sedighi. "Elastic Thermal Deformation of an Infinite Copper Material Due to Cyclic Heat Supply Using Higher-Order Nonlocal Thermal Modeling." Metals 12, no. 11 (November 10, 2022): 1927. http://dx.doi.org/10.3390/met12111927.

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Thermoelastic modeling at nanoscale is becoming more important as devices shrink and heat sources are more widely used in modern industries, such as nanoelectromechanical systems. However, the conventional thermoelastic theories are no longer applicable in high-temperature settings. This study provides an insight into the thermomechanical features of a nonlocal viscous half-space exposed to a cyclic heat source. Using a novel concept of fractional derivatives, introduced by Atangana and Baleanu, it is assumed that the viscoelastic properties follow the fractional Kelvin–Voigt model. The nonlocal differential form of Eringen’s nonlocal theory is employed to consider the impact of small-scale behavior. It is also proposed that the rule of dual-phase thermal conductivity can be generalized to thermoelastic materials to include the higher-order time derivatives. The numerical results for the examined physical variables are presented using the Laplace transform technique. Furthermore, several numerical analyses are performed in-depth, focusing on the effects of nonlocality, structural viscoelastic indicator, fractional order, higher-order and phase-lag parameters on the behavior of the nanoscale half-space. According to the presented findings, it appears that the higher-order terms have a major impact on reactions and may work to mitigate the impact of thermal diffusion. Furthermore, these terms provide a novel approach to categorize the materials based on their thermal conductivities.
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42

Uzun, Büşra, and Ömer Civalek. "Nonlocal FEM Formulation for Vibration Analysis of Nanowires on Elastic Matrix with Different Materials." Mathematical and Computational Applications 24, no. 2 (April 6, 2019): 38. http://dx.doi.org/10.3390/mca24020038.

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In this study, free vibration behaviors of various embedded nanowires made of different materials are investigated by using Eringen’s nonlocal elasticity theory. Silicon carbide nanowire (SiCNW), silver nanowire (AgNW), and gold nanowire (AuNW) are modeled as Euler–Bernoulli nanobeams with various boundary conditions such as simply supported (S-S), clamped simply supported (C-S), clamped–clamped (C-C), and clamped-free (C-F). The interactions between nanowires and medium are simulated by the Winkler elastic foundation model. The Galerkin weighted residual method is applied to the governing equations to gain stiffness and mass matrices. The results are given by tables and graphs. The effects of small-scale parameters, boundary conditions, and foundation parameters on frequencies are examined in detail. In addition, the influence of temperature change on the vibrational responses of the nanowires are also pursued as a case study.
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43

Mirzade, F. "Size Effects on Surface Elastic Waves in a Semi-Infinite Medium with Atomic Defect Generation." Advances in Condensed Matter Physics 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/528208.

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The paper investigates small-scale effects on the Rayleigh-type surface wave propagation in an isotopic elastic half-space upon laser irradiation. Based on Eringen’s theory of nonlocal continuum mechanics, the basic equations of wave motion and laser-induced atomic defect dynamics are derived. Dispersion equation that governs the Rayleigh surface waves in the considered medium is derived and analyzed. Explicit expressions for phase velocity and attenuation (amplification) coefficients which characterize surface waves are obtained. It is shown that if the generation rate is above the critical value, due to concentration-elastic instability, nanometer sized ordered concentration-strain structures on the surface or volume of solids arise. The spatial scale of these structures is proportional to the characteristic length of defect-atom interaction and increases with the increase of the temperature of the medium. The critical value of the pump parameter is directly proportional to recombination rate and inversely proportional to deformational potentials of defects.
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44

Shojaeefard, Mohammad Hassan, Hamed Saeidi Googarchin, Mohammad Mahinzare, and Seyed Ahmad Eftekhari. "Magnetic field effect on free vibration of smart rotary functionally graded nano/microplates: A comparative study on modified couple stress theory and nonlocal elasticity theory." Journal of Intelligent Material Systems and Structures 29, no. 11 (April 27, 2018): 2492–507. http://dx.doi.org/10.1177/1045389x18770875.

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In this article, free vibration behavior of a rotating nano/microcircular plate constructed from functionally graded magneto-elastic material is simulated with the first-order shear deformation theory. For the sake of comparison, the nonlocal elasticity theory and the modified couple stress theory are employed to implement the small size effect in the natural frequencies behavior of the nano/microcircular plate. The governing equations of motion for functionally graded magneto-elastic material nano/microcircular plates are derived based on Hamilton’s principle; comparing the obtained results with those in the literature, they are in a good agreement. Finally, the governing equations are solved using the differential quadrature method. It is shown that the vibrational characteristics of functionally graded magneto-elastic material nano/microcircular plates are significantly affected by non-dimensional angular velocity, size dependency of the Eringen’s and the modified couple stress theories, and power law index for clamped and hinged boundary conditions. Results show that a critical point occurs by increasing the angular velocity and the effect of several parameters are changed after this point.
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45

Selvamani, Rajendran, M. Mahaveer Sree Jayan, and Farzad Ebrahimi. "Nonlinear ultrasonic waves in a magneto-flexo-thermally actuated single walled armchair carbon nanotube embedded on polymer matrix." World Journal of Engineering 18, no. 1 (November 23, 2020): 1–13. http://dx.doi.org/10.1108/wje-02-2020-0066.

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Purpose The purpose of this paper is concerned with the study of nonlinear ultrasonic waves in a magneto-flexo-thermo (MFT) elastic armchair single-walled carbon nanotube (ASWCNT) resting on polymer matrix. Design/methodology/approach A mathematical model is developed for the analytical study of nonlinear ultrasonic waves in a MFT elastic armchair single walled carbon nanotube rested on polymer matrix using Euler beam theory. The analytical formulation is developed based on Eringen’s nonlocal elasticity theory to account small scale effect. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been analysed numerically by using the nonlinear foundations supported by Winkler-Pasternak model. The solution is obtained by ultrasonic wave dispersion relations. Findings From the literature survey, it is evident that the analytical formulation of nonlinear ultrasonic waves in an MFT elastic ASWCNT embedded on polymer matrix is not discussed by any researchers. So, in this paper the analytical solutions of nonlinear ultrasonic waves in an MFT elastic ASWCNT embedded on polymer matrix are studied. Parametric studies is carried out to scrutinize the influence of the nonlocal scaling, magneto-electro-mechanical loadings, foundation parameters, various boundary condition and length on the dimensionless frequency of nanotube. It is noticed that the boundary conditions, nonlocal parameter and tube geometrical parameters have significant effects on dimensionless frequency of nanotubes. Originality/value This paper contributes the analytical model to find the solution of nonlinear ultrasonic waves in an MFT elastic ASWCNT embedded on polymer matrix. It is observed that the increase in the foundation constants raises the stiffness of the medium and the structure is able to attain higher frequency once the edge condition is C-C followed by S-S. Further, it is noticed that the natural frequency is arrived below 1% in both local and nonlocal boundary conditions in the presence of temperature coefficients. Also, it is found that the density and Poisson ratio variation affects the natural frequency with below 2%. The results presented in this study can provide mechanism for the study and design of the nano devices such as component of nano oscillators, micro wave absorbing, nano-electron technology and nano-electro--magneto-mechanical systems that make use of the wave propagation properties of ASWCNTs embedded on polymer matrix.
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46

Sae-Long, Worathep, Suchart Limkatanyu, Woraphot Prachasaree, Jaroon Rungamornrat, and Piti Sukontasukkul. "A Thermodynamics-Based Nonlocal Bar-Elastic Substrate Model with Inclusion of Surface-Energy Effect." Journal of Nanomaterials 2020 (May 16, 2020): 1–16. http://dx.doi.org/10.1155/2020/8276745.

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This paper presents a bar-elastic substrate model to investigate the axial responses of nanowire-elastic substrate systems considering the effects of nonlocality and surface energy. The thermodynamics-based strain gradient model is adopted to capture the nonlocality of the bar-bulk material while the Gurtin-Murdoch surface theory is utilized to consider the surface energy. To characterize the bar-surrounding substrate interaction, the Winkler foundation model is employed. In a direct manner, system compatibility conditions are obtained while within the framework of the virtual displacement principle, the system equilibrium condition and the corresponding natural boundary conditions are consistently obtained. Three numerical simulations are conducted to investigate the characteristics and behaviors of the nanowire-elastic substrate system: the first is conducted to reveal the capability of the proposed model to eliminate the paradoxical behavior inherent to the Eringen nonlocal differential model; the second is employed to characterize responses of the nanowire-elastic substrate system; and the third is aimed at demonstrating the dependence of the system effective Young’s modulus on several system parameters.
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47

Firouz-Abadi, Rohollah Dehghani, Hassan Mohammad-Khani, and Mohammad Rahmanian. "Vibration and Stability Analysis of DWCNT-Based Spinning Nanobearings." International Journal of Structural Stability and Dynamics 17, no. 09 (October 23, 2017): 1750102. http://dx.doi.org/10.1142/s0219455417501024.

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This paper aims at investigating free vibrations and stability of double-walled carbon nanotube (DWCNT)-based spinning nanobearings. The so-called nanobearing consists of two coaxial carbon nanotubes (CNTs) where either of the two CNTs can be a rotor while the other takes the role of stator. Euler–Bernoulli beam model along with the Eringen’s nonlocal theory of elasticity are employed to obtain governing equations of transverse vibrations for the CNTs. The coupling of the two CNTs originates from the van-der-Waals (vdW) forcing present in the interface of the two CNTs. The coupling is taken into account as distributed spring foundation with an equivalent elastic stiffness. Based on the obtained model, effects of small-scale parameter, vdW interaction between CNTs and the diameter ratio of CNTs on the critical spinning speed are investigated. Finally, the stability margins of the nanobearings are determined and some general conclusions are drawn.
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48

Jena, Subrat Kumar, and S. Chakraverty. "Dynamic Analysis of Single-Layered Graphene Nano-Ribbons (SLGNRs) with Variable Cross-Section Resting on Elastic Foundation." Curved and Layered Structures 6, no. 1 (January 1, 2019): 132–45. http://dx.doi.org/10.1515/cls-2019-0011.

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AbstractThis article deals with free vibration of the variable cross-section (non-uniform) single-layered graphene nano-ribbons (SLGNRs) resting on Winkler elastic foundation using the Differential Quadrature Method (DQM). Here characteristic width of the cross-section is varied exponentially along the length of the nano-ribbon while the thickness of the cross section is kept constant. Euler–Bernoulli beam theory in conjunction with Eringen nonlocal elasticity theory is considered in this study. The numerical as well as graphical results are reported by using MATLAB codes developed by authors. Convergence of present method is explored and our results are compared with known results available in literature showing excellent agreement. Further, effects various parameters on frequency parameters are studied comprehensively.
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49

Arani, A. Ghorbanpour, Z. Khoddami Maraghi, and H. Khani Arani. "Orthotropic patterns of Pasternak foundation in smart vibration analysis of magnetostrictive nanoplate." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, no. 4 (April 9, 2015): 559–72. http://dx.doi.org/10.1177/0954406215579929.

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In this research, free vibration of rectangular nanoplate made of magnetostrictive materials is studied while it is focused on elastic medium as an efficient stability factor. For this purpose, Pasternak foundation is developed by considering orthotropy angle where the effect of Pasternak shear modulus is investigated in different directions. Since the nanoplate is subjected to the coil, a feedback control system follows the effects of uniform magnetic field on vibration characteristics of magnetostrictive nanoplate. So, Reddy’s third-order shear deformation theory along with Eringen’s nonlocal continuum model are utilized in order to derive motion equations at nanoscale using Hamilton’s principle. Five coupled motion equations solved by differential quadrature method in two-dimensional space by considering different boundary conditions. Results indicate that with appropriative selection for orthotropy angle, normal, and shear Pasternak foundation modulus, it is possible to achieve optimal and desire values to more stability of magnetostrictive nanoplate. These findings can be used in automotive industry, communications equipment in nano- and microstructures.
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50

Ziaee, Sima. "Postbuckling and nonlinear free vibration of size-dependent prestressed FG nanobeams resting on elastic foundation based on nonlocal Euler-Bernoulli beam theory." Journal of the Mechanical Behavior of Materials 24, no. 3-4 (August 1, 2015): 91–103. http://dx.doi.org/10.1515/jmbm-2015-0011.

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AbstractVibrations of micro/nanobeams that are subjected to initial stresses due to mismatch between different materials or thermal stresses are important in some devices. The present study is an attempt to present nonlinear free vibration of simply supported size-dependent functionally graded (FG) nanobeams resting on elastic foundation and under precompressive axial force. It is assumed that the material properties of FG materials are graded in the thickness direction. The partial differential equation of motion, which is simplified into an ordinary differential equation using the Galerkin method, is derived based on Euler-Bernoulli beam theory, von Karman geometric nonlinearity, and Eringen’s nonlocal elasticity theory. The final ordinary differential equation is solved using the variational iteration method. The effects of geometrical parameters, small-scale parameter, elastic coefficient of foundation, precompressive axial force, and neutral axis location on dimensionless nonlinear natural frequencies are investigated. In this study, the buckling and postbuckling behavior of FG nanobeams and the effect of neutral axis location on buckling behavior are investigated as well. Results show that the effects of small scale on FG nanobeam frequencies change with the aspect ratio, the values of radius of gyration, and the values of compressive axial force. It is also found that the influence of neutral axis location on the nonlinear fundamental frequency of prestressed FG nanobeams is more than that of prestressed FG nanobeams resting on elastic foundation.
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