• Title/Summary/Keyword: Nonlocal condition

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A review of effects of partial dynamic loading on dynamic response of nonlocal functionally graded material beams

  • Ahmed, Ridha A.;Fenjan, Raad M.;Hamad, Luay Badr;Faleh, Nadhim M.
    • Advances in materials Research
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    • v.9 no.1
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    • pp.33-48
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    • 2020
  • With the use of differential quadrature method (DQM), forced vibrations and resonance frequency analysis of functionally graded (FG) nano-size beams rested on elastic substrate have been studied utilizing a shear deformation refined beam theory which contains shear deformations influence needless of any correction coefficient. The nano-size beam is exposed to uniformly-type dynamical loads having partial length. The two parameters elastic substrate is consist of linear springs as well as shear coefficient. Gradation of each material property for nano-size beam has been defined in the context of Mori-Tanaka scheme. Governing equations for embedded refined FG nano-size beams exposed to dynamical load have been achieved by utilizing Eringen's nonlocal differential law and Hamilton's rule. Derived equations have solved via DQM based on simply supported-simply supported edge condition. It will be shown that forced vibrations properties and resonance frequency of embedded FG nano-size beam are prominently affected by material gradation, nonlocal field, substrate coefficients and load factors.

Free axial vibration analysis of axially functionally graded thick nanorods using nonlocal Bishop's theory

  • Nazemnezhad, Reza;Kamali, Kamran
    • Steel and Composite Structures
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    • v.28 no.6
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    • pp.749-758
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    • 2018
  • Free axial vibration of axially functionally graded (AFG) nanorods is studied by focusing on the inertia of lateral motions and shear stiffness effects. To this end, Bishop's theory considering the inertia of the lateral motions and shear stiffness effects and the nonlocal theory considering the small scale effect are used. The material properties are assumed to change continuously through the length of the AFG nanorod according to a power-law distribution. Then, nonlocal governing equation of motion and boundary conditions are derived by implementing the Hamilton's principle. The governing equation is solved using the harmonic differential quadrature method (HDQM), After that, the first five axial natural frequencies of the AFG nanorod with clamped-clamped end condition are obtained. In the next step, effects of various parameters like the length of the AFG nanorod, the diameter of the AFG nanorod, material properties, and the nonlocal parameter value on natural frequencies are investigated. Results of the present study can be useful in more accurate design of nano-electro-mechanical systems in which nanotubes are used.

Nonlinear vibration analysis of a nonlocal sinusoidal shear deformation carbon nanotube using differential quadrature method

  • Pour, Hasan Rahimi;Vossough, Hossein;Heydari, Mohammad Mehdi;Beygipoor, Gholamhossein;Azimzadeh, Alireza
    • Structural Engineering and Mechanics
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    • v.54 no.6
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    • pp.1061-1073
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    • 2015
  • This paper presents a nonlocal sinusoidal shear deformation beam theory (SDBT) for the nonlinear vibration of single walled carbon nanotubes (CNTs). The present model is capable of capturing both small scale effect and transverse shear deformation effects of CNTs, and does not require shear correction factors. The surrounding elastic medium is simulated based on Pasternak foundation. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the CNTs are derived using Hamilton's principle. Differential quadrature method (DQM) for the natural frequency is presented for different boundary conditions, and the obtained results are compared with those predicted by the nonlocal Timoshenko beam theory (TBT). The effects of nonlocal parameter, boundary condition, aspect ratio on the frequency of CNTs are considered. The comparison firmly establishes that the present beam theory can accurately predict the vibration responses of CNTs.

POSITIVE SOLUTIONS FOR THE SECOND ORDER DIFFERENTIAL SYSTEM WITH STRONGLY COUPLED INTEGRAL BOUNDARY CONDITION

  • You-Young Cho;Jinhee Jin;Eun Kyoung Lee
    • East Asian mathematical journal
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    • v.40 no.1
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    • pp.37-50
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    • 2024
  • We establish the existence, multiplicity and uniqueness of positive solutions to nonlocal boundary value systems with strongly coupled integral boundary condition by using the global continuation theorem and Banach's contraction principle.

EXISTENCE AND CONTROLLABILITY RESULTS FOR NONDENSELY DEFINED STOCHASTIC EVOLUTION DIFFERENTIAL INCLUSIONS WITH NONLOCAL CONDITIONS

  • Ni, Jinbo;Xu, Feng;Gao, Juan
    • Journal of the Korean Mathematical Society
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    • v.50 no.1
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    • pp.41-59
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    • 2013
  • In this paper, we investigate the existence and controllability results for a class of abstract stochastic evolution differential inclusions with nonlocal conditions where the linear part is nondensely defined and satisfies the Hille-Yosida condition. The results are obtained by using integrated semigroup theory and a fixed point theorem for condensing map due to Martelli.

Small scale effect on the vibration of non-uniform nanoplates

  • Chakraverty, S.;Behera, Laxmi
    • Structural Engineering and Mechanics
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    • v.55 no.3
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    • pp.495-510
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    • 2015
  • Free vibration of non-uniform embedded nanoplates based on classical (Kirchhoff's) plate theory in conjunction with nonlocal elasticity theory has been studied. The nanoplate is assumed to be rested on two-parameter Winkler-Pasternak elastic foundation. Non-uniform material properties of nanoplates have been considered by taking linear as well as quadratic variations of Young's modulus and density along the space coordinates. Detailed analysis has been reported for all possible casesof such variations. Trial functions denoting transverse deflection of the plate are expressed in simple algebraic polynomial forms. Application of the present method converts the problem into generalised eigen value problem. The study aims to investigate the effects of non-uniform parameter, elastic foundation, nonlocal parameter, boundary condition, aspect ratio and length of nanoplates on the frequency parameters. Three-dimensional mode shapes for some of the boundary conditions have also been illustrated. One may note that present method is easier to handle any sets of boundary conditions at the edges.

Controllability for the Semilinear Fuzzy Integrodifferential Equations with Nonlocal Conditions and Forcing Term with Memory (기억을 갖는 강제항과 비국소조건을 갖는 준선형 퍼지 적분미분방정식에 대한 제어가능성)

  • Kwun, Young-Chel;Ahn, Young-Chel;Park, Dong-Gun;Kim, Seon-Yu
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2007.04a
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    • pp.213-216
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    • 2007
  • In this paper. we study the controllability for the semilinear fuzzy integrodifferential equations with nonlocal condition and forcing term with memory in $E_N$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in $E_N$.

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APPROXIMATIONS OF SOLUTIONS FOR A NONLOCAL FRACTIONAL INTEGRO-DIFFERENTIAL EQUATION WITH DEVIATED ARGUMENT

  • CHADHA, ALKA;PANDEY, DWIJENDRA N.
    • Journal of applied mathematics & informatics
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    • v.33 no.5_6
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    • pp.699-721
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    • 2015
  • This paper investigates the existence of mild solution for a fractional integro-differential equations with a deviating argument and nonlocal initial condition in an arbitrary separable Hilbert space H via technique of approximations. We obtain an associated integral equation and then consider a sequence of approximate integral equations obtained by the projection of considered associated nonlocal fractional integral equation onto finite dimensional space. The existence and uniqueness of solutions to each approximate integral equation is obtained by virtue of the analytic semigroup theory via Banach fixed point theorem. Next we demonstrate the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. We consider the Faedo-Galerkin approximation of the solution and demonstrate some convergenceresults. An example is also given to illustrate the abstract theory.