Nonlocal theory
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In this study two types of MEE plates, namely BaTiO3 and CoFe2O4 were considered. The basic equations are derived using classical plate theory with nonlocal stress theory and are solved using the Galerkin method and Runge-Kutta method.
13p viambani 18-06-2024 1 1 Download
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In this paper, the free vibration of a bi-directional functionally graded (2D-FG) nanobeams is investigated by the finite element method. Nanobeams are made of two kinds of porous materials. The material properties of 2D-FG nanobeams are assumed to vary in both axial and thickness directions according to a power law . Based on Eringen's nonlocal elasticity theory, the governing equations of motion are derived.
10p dathienlang1012 03-05-2024 0 0 Download
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In this study, the nonlocal elasticity theory is applied to analyze the free vibration of the functionally graded nanobeams. The novelty of the present study is that the classical nonlocal elasticity theory has been modified to take into account the variation of the nonlocal parameters through the thickness of the functionally graded. nanobeams.
10p dathienlang1012 03-05-2024 1 0 Download
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The article "Static behavior of FGP half-annular nanoplates resting on elastic foundation using nonlocal elasticity theory" presents an algorithm finite element for static bending analysis of the functionally graded porous (FGP) half-annular nanoplate resting on the elastic foundation (EF) using nonlocal elasticity theory. The FGP materials with two-parameter are the volume fraction index (k) and the porosity volume fraction (5) in two cases of even and uneven porosity. The EF includes Winkler-stiffness (k₁) and Pasternak- stiffness (k₂).
9p dathienlang1012 03-05-2024 3 0 Download
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The paper "Nonlinear vibration of functionally graded porous micro-beams resting on elastic foundation" presents the analysis of nonlinear vibration of functionally graded porous (FGP) micro-beams resting on an elastic foundation. The Euler-Bernoulli beam theory (EBT) and the nonlocal strain gradient theory (NSGT) are considered to establish the equations of motion of the micro-beam. The material properties of the micro-beam are assumed to be changed continuously along thickness direction according to simple power-law distribution.
9p dathienlang1012 03-05-2024 0 0 Download
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In this paper, we considered the propagation wave in transversely isotropic piezoelastic medium based on the nonlocal strain gradient theory. Two kinds of scale parameters, namely, the nonlocal parameter and the strain gradient parameter are introduced to account for the size effect of mechanical properties of nanostructures.
18p dianmotminh02 03-05-2024 6 2 Download
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This article presents a finite element method for static bending analysis of the functionally graded porous (FGP) L-shape nanoplate resting on the elastic foundation (EF) using the nonlocal elasticity theory.
9p vimarillynhewson 02-01-2024 12 2 Download
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This paper analyses free vibrations of framed nanostructures made of Functionally Graded Material (FGM) based on the Nonlocal Elastic Theory (NET) and the Dynamic Stiffness Method (DSM). FGM characteristics vary nonlinearly throughout the height of the beam element.
19p viisac 15-09-2023 11 3 Download
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This article presents an application of finite element algorithm for static bending analysis of the functionally graded porous (FGP) annular nanoplate resting on the elastic foundation (EF) using nonlocal elasticity theory.
10p viengels 25-08-2023 4 3 Download
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In this paper, the free vibration of twodimensional functionally graded (2D-FG) sandwich nanobeam is investigated by the finite element method. The material properties of 2D-FG sandwich nanobeam are assumed to vary in both axial and thickness directions according to a power law. Based on Eringen's nonlocal elasticity theory, the governing equations of motion are derived.
7p visirius 18-01-2023 4 2 Download
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Based on nonlocal strain gradient theory approach, we have analyzed the nonlinear dynamic response and vibration of sandwich thick plates with functionally graded (FG) face sheets and FG porous core subjected to mechanical, thermal and blast loads on elastic foundations.
15p vimelindagates 18-07-2022 12 3 Download
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In this paper, the nonlocal elasticity theory is applied to study the propagation of plane wave and Rayleigh-type surface wave in an incompressible, rotating and transversely isotropic material. The governing equations of motion for an incompressible, rotating, transversely isotropic and nonlocal elastic medium are specialized for a plane. The medium is assumed rotating about an axis perpendicular to the plane. The transverse isotropy axis is taken perpendicular to the surface.
16p inception36 30-11-2021 8 1 Download
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Vibration analysis of functionally graded nano beams with different boundary conditions is presented in this paper. The first-order shear deformation theory and nonlocal elasticity theory are used to incorporate size small effect of functionally graded nano beams. Ritz-type analytical solution is used to solve the characteristic equations of motion for different boundary conditions.
8p viwendy2711 05-10-2021 16 1 Download
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The nonlinear free vibration of embedded nanotubes under longitudinal magnetic field is studied in this paper. The governing equation for the nanotube is formulated by employing Euler–Bernoulli beam model and the nonlocal strain gradient theory. The analytical expression of the nonlinear frequency of the nanotube is obtained by using Galerkin method and the equivalent linearization method with the weighted averaging value. The accuracy of the obtained solution has been verified by comparison with the published solutions and the exact solution.
23p nguaconbaynhay11 07-04-2021 19 2 Download
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In this paper, we present a result on Hyers-Ulam stability for a class of nonlocal differential equations in Hilbert spaces by using the theory of integral equations with completely positive kernels together with a new Gronwall inequality type. The paper develops some recent results on fractional differential equations to the ones involving general nonlocal derivatives. Instead of Mittag-Leffler functions, we must utilize the characterization of relaxation function.
7p tamynhan5 10-12-2020 11 2 Download
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This paper presents free vibration analysis of functionally graded (FG) porous nanoplates based on isogeometric approach. Based on a modified power-law function, material properties are given. The nonlocal elasticity is used to capture size effects. According to a combination of the Hamilton’s principle and the higher order shear deformation theory, the governing equations of the porous nanoplates are derived.
11p angicungduoc5 13-06-2020 16 0 Download
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Fractional calculus (FC) is widely used in many interdisciplinary branches of science due to its effectiveness in describing and investigating complicated phenomena. In this work, nonlinear dynamics for a new physical model using nonlocal fractional differential operator with singular kernel is introduced. New Routh-Hurwitz stability conditions are derived for the fractional case as the order lies in [0,2). The new and basic Routh-Hurwitz conditions are applied to the commensurate case. The local stability of the incommensurate orders is also discussed.
12p covid19 14-06-2020 27 2 Download
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In the present paper, the differential transformation method is employed to develop a semi-analytical solution for free transverse vibration of single-walled carbon nanotube (SWCNT) with arbitrary boundary conditions.
14p tohitohi 19-05-2020 10 0 Download
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The next chapter presents an analytical solution for a nano-plate with Levy boundary conditions. The free vibration analysis is based on a first order shear deformation theory which includes the small scale effect. The governing equations of motion, reformulated as two new equations called the edge-zone and interior equations, are based on the nonlocal constitutive equations of Eringen.
290p lulanphuong 30-03-2012 79 16 Download
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MAXIMUM PRINCIPLES FOR A FAMILY OF NONLOCAL BOUNDARY VALUE PROBLEMS PAUL W. ELOE Received 21 October
MAXIMUM PRINCIPLES FOR A FAMILY OF NONLOCAL BOUNDARY VALUE PROBLEMS PAUL W. ELOE Received 21 October 2003 and in revised form 16 February 2004 We study a family of three-point nonlocal boundary value problems (BVPs) for an nthorder linear forward difference equation. In particular, we obtain a maximum principle and determine sign properties of a corresponding Green function. Of interest, we show that the methods used for two-point disconjugacy or right-disfocality results apply to this family of three-point BVPs. 1.
10p sting12 10-03-2012 21 4 Download