Elastic foundation effect on nonlinear thermo-vibration of embedded double-layered orthotropic graphene sheets using differential quadrature method

Arani, A. Ghorbanpour; Kolahchi, Reza; Barzoki, A.A. Mosallaie; Mozdianfard, Mohammad Reza; Farahani, S Mosatafa Noudeh

doi:10.1177/0954406212453808

Cited by 48 publications

(15 citation statements)

References 35 publications

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“…It was primarily developed by Richard Bellman and his associates in the early 1970s [36]. In DQM, the differential equations are changed into a first-order algebraic equation by employing appropriate weighting coefficients because weighting coefficients do not relate to any special problem and only depend on the grid spacing [37].…”

Section: The Methods Of Differential Quadraturementioning

confidence: 99%

Natural frequency analysis of functionally graded material truncated conical shell with lengthwise material variation based on first-order shear deformation theory

Asanjarani

Kargarnovin

Satouri

et al. 2015

Mechanics of Advanced Materials and Structures

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Based on the First order Shear Deformation Theory (FSDT), the free vibration of the functionally graded (FG) truncated conical shells is analyzed. The truncated conical shell materials are assumed to be isotropic and inhomogeneous in the longitudinal direction. The twoconstituent (FG) shell consists of ceramic and metal. These constituents are graded through the length, from one end of the shell to the other end. Using Hamilton's principle the derived governing equations are solved using Differential Quadrature Method (DQM). Fast rate of convergence of this method is tested and its advantages over other existing solver methods are observed. The primary results of this study were obtained for four different ends boundary conditions and for some special cases acquire results were compared with those available in the * Graduate Student † Corresponding author, (Ali.Asanjarani@Gmail.com) Downloaded by [University of Connecticut] at 20:02 11 April 2015 ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT 2 literature. Furthermore, effects of geometrical parameters, material graded power index, and boundary conditions on the natural frequencies of the FG truncated conical shell are carried out.

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Section: The Methods Of Differential Quadraturementioning

confidence: 99%

Natural frequency analysis of functionally graded material truncated conical shell with lengthwise material variation based on first-order shear deformation theory

Asanjarani

Kargarnovin

Satouri

et al. 2015

Mechanics of Advanced Materials and Structures

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“…Therefore, the governing equations and boundary conditions are discretized by means of the aforementioned method. 61,65 In this investigation, the cosine pattern is employed to generate the DQ point system as the following form…”

Section: Nonlinear Vibration Analysismentioning

confidence: 99%

Influence of flexoelectric, small-scale, surface and residual stress on the nonlinear vibration of sigmoid, exponential and power-law FG Timoshenko nano-beams

Arefi

Pourjamshidian

Arani

et al. 2018

Journal of Low Frequency Noise, Vibration and Active Control

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This research deals with the nonlinear vibration of the functionally graded nano-beams based on the nonlocal elasticity theory considering surface and flexoelectric effects. The flexoelectric functionally graded nano-beam is resting on nonlinear Pasternak foundation. Cubic nonlinearity is assumed for foundation. It is assumed that the material properties of the nano-beam change continuously along the thickness direction according to different patterns of material distribution. In order to include coupling of strain gradients and electrical polarizations in equation of motion, the nonlocal, nonclassical nano-beam model containing flexoelectric effect is employed. In addition, the effects of surface elasticity, di-electricity, and piezoelectricity as well as bulk flexoelectricity are accounted in constitutive relations. The governing equations of motion are derived using Hamilton principle based on first shear deformation beam theory and the nonlocal strain gradient elasticity theory considering residual surface stresses. The differential quadrature method is used to calculate nonlinear natural frequency of flexoelectric functionally graded nano-beam as well as nonlinear vibrational mode shape. After validation of the present numerical results with those results available in literature, full numerical results are presented to investigate the influence of important parameters such as flexoelectric coefficients of the surface and bulk, residual surface stresses, nonlocal parameter, length scale effects (strain gradient parameter), cubic nonlinear Winkler and shear coefficients, power gradient index of functionally graded material, and geometric dimensions on the nonlinear vibration behaviors of flexoelectric functionally graded nano-beam. The numerical results indicate that, considering the flexoelectricity leads to the decrease of the bending stiffness of the flexoelectric functionally graded nano-beams.

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“…Based on the classical plate theory (CPT) which satisfies Kirchhoff assumption, the strain equations in terms of the midplane displacements are derived as follows [13]…”

Section: A Classical Plate Theorymentioning

confidence: 99%

Nonlocal vibration behavior of a Pasternak bonded double-piezoelectric-DWBNNT-reinforced microplate-system

2014

International Conference on Machine Learning, Electrical and Mechanical Engineering (ICMLEME'2014) Jan. 8-9, 2014 Dubai (UAE)

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The aim of the paper is to analyze electro-thermo nonlinear vibration of a double-piezoelectric composite microplatesystem (DPCMPS) based on nonlocal piezoelasticity theory. The two microplates are assumed to be connected by an enclosing elastic medium which is simulated by Pasternak foundation. Both of piezoelectric composite microplates are made of poly-vinylidene fluoride (PVDF) reinforced by zigzag double walled boron nitride nanotubes (DWBNNTs). The micro-electromechanical model is employed to calculate mechanical, thermal and electrical properties of composite. Differential quadrature method (DQM) is employed to solve the governing differential equations. The frequency ratio of DPCMPS is investigated for three typical vibrational states, namely, out-of-phase, in-phase and the case when one microplate is fixed in the DPCMPS. A detailed parametric study is conducted to scrutinize the influences of the small scale coefficient and stiffness of the internal elastic medium.

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Elastic foundation effect on nonlinear thermo-vibration of embedded double-layered orthotropic graphene sheets using differential quadrature method

Cited by 48 publications

References 35 publications

Natural frequency analysis of functionally graded material truncated conical shell with lengthwise material variation based on first-order shear deformation theory

Natural frequency analysis of functionally graded material truncated conical shell with lengthwise material variation based on first-order shear deformation theory

Influence of flexoelectric, small-scale, surface and residual stress on the nonlinear vibration of sigmoid, exponential and power-law FG Timoshenko nano-beams

Nonlocal vibration behavior of a Pasternak bonded double-piezoelectric-DWBNNT-reinforced microplate-system

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