Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams

Ke, Liao-Liang; Yang, Jie; Kitipornchai, S.

doi:10.1016/j.compstruct.2009.09.024

Cited by 512 publications

(176 citation statements)

References 34 publications

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“…Similarly, the effective thermal expansion coefficients in the longitudinal and transverse directions (α 11 (11) It is assumed that the material properties of CNTs and matrix are the functions of temperature, so that the effective material properties of FG-CNTRCs, like Young's modulus, shear modulus and thermal expansion coefficients, are also functions of temperature T and position z.…”

Section: Materials Properties Of Cntrc Beamsmentioning

confidence: 99%

“…Yang and Chen [10] investigated free vibration and buckling analysis of FGM beam with open crack at their edge by using BernoulliEuler beam theory and the rotation spring model. LiaoLiang Ke et al [11] investigated the nonlinear free vibration of functionally graded nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) based on Timoshenko beam theory.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear free vibration analysis of elastically supported carbon nanotube-reinforced composite beam with the thermal environment in non-deterministic framework

Chaudhari¹,

Shegokar²,

Lal

2017

Curved and Layered Structures

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This paper deals with the investigation of nonlinear free vibration behavior of elastically supported carbon nanotube reinforced composite (CNTRC) beam subjected to thermal loading with random system properties. Material properties of each constituent's material, volume fraction exponent and foundation parameters are considered as uncorrelated Gaussian random input variables. The beam is supported by a Pasternak foundation with Winkler cubic nonlinearity. The higher order shear deformation theory (HSDT) with von-Karman nonlinearity is used to formulate the governing equation using Hamilton principle. Convergence and validation study is carried out through the comparison with the available results in the literature for authenticity and accuracy of the present approach used in the analysis. First order perturbation technique (FOPT),Second order perturbation technique (SOPT) and Monte Carlo simulation (MCS) methods are employed to investigate the effect of geometric configuration, volume fraction exponent, foundation parameters, distribution of reinforcement and thermal loading on nonlinear vibration characteristics CNTRC beam.The present work signifies the accurate analysis of vibrational behaviour influences by different random variables. Results are presented in terms of mean, variance (COV) and probability density function (PDF) for various aforementioned parameters.

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Section: Materials Properties Of Cntrc Beamsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear free vibration analysis of elastically supported carbon nanotube-reinforced composite beam with the thermal environment in non-deterministic framework

Chaudhari¹,

Shegokar²,

Lal

2017

Curved and Layered Structures

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show abstract

“…Those who included nonlinearity in either the geometry or the actuating force for CNTs are few [11][12][13][14][15][16][17]. To mention some, Hosseini-Ara et al [11] proposed analytical solutions based on nonlocal Timoshenko kinematics, strain gradient approach and some variational methods to derive the higher-order boundary conditions as well as governing for the sake of investigating the buckling characteristics of CNTs.…”

Section: Introductionmentioning

confidence: 99%

“…Mehdipour et al [16] investigated the use electrostatically actuated clamped-free CNT with an attached mass as a bio-mass sensor. Ke et al [17] investigated the nonlinear free vibration problem …”

Section: Introductionmentioning

confidence: 99%

Nonlocal modeling of a Carbon Nanotube actuated by an electrostatic force

2016

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Abstract. Carbon nanotubes (CNTs) are promising mechanical structures at the nano-scale which have attracted increasing attention due to their amazing mechanical, chemical, thermal, and electrical properties. To take into account size dependence of such small sized structures, the use of nonlocal continuum theory is proposed where intrinsic length scales is taken into account. Based on the Eringen theory, a nonlinear nonlocal model of a clamped-clamped CNT is developed in this study. Static and free vibration responses are simulated and analyzed. The main objective of this work is to study the influence of CNT size and length scale parameter on the static and free vibration response to better understand their effect on the general behavior of the CNT. It has been found that the nonlocal effect can largely influence the performance of the CNT and change qualitatively its nonlinear response.

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“…Rafiee et al [2] analyzed large amplitude free vibration of functionally graded carbon nanotube reinforced composite beams with surfacebonded piezoelectric layers based on the Euler-Bernoulli beam theory. The geometric nonlinear free vibration of FG-CNT beams was investigated by Ke et al [3] using the Timoshenko beam theory and von Kármán geometric nonlinearity. Later, Ke and his co-authors [4] considered the size effect and investigated the bending, buckling and vibration behavior of functionally graded micro plates.…”

Section: Introductionmentioning

confidence: 99%

Vibration characteristics of functionally graded carbon nanotube reinforced composite rectangular plates on Pasternak foundation with arbitrary boundary conditions and internal line supports

Zhong

Wang

Tang

et al. 2018

Curved and Layered Structures

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This paper presents the first known vibration characteristics of moderately thick functionally graded carbon nanotube reinforced composite rectangular plates on Pasternak foundation with arbitrary boundary conditions and internal line supports on the basis of the firstorder shear deformation theory. Different distributions of single walled carbon nanotubes (SWCNTs) along the thickness are considered. Uniform and other three kinds of functionally graded distributions of carbon nanotubes along the thickness direction of plates are studied. The solutions carried out using an enhanced Ritz method mainly include the following three points: Firstly, create the Lagrange energy function by the energy principle; Secondly, as the main innovation point, the modified Fourier series are chosen as the basic functions of the admissible functions of the plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges; Lastly, solve the natural frequencies as well as the associated mode shapes by means of the Ritz-variational energy method. In this study, the influences of the volume fraction of CNTs, distribution type of CNTs, boundary restrain parameters, location of the internal line supports, foundation coefficients on the natural frequencies and mode shapes of the FG-CNT reinforced composite rectangular plates are presented.

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Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams

Cited by 512 publications

References 34 publications

Nonlinear free vibration analysis of elastically supported carbon nanotube-reinforced composite beam with the thermal environment in non-deterministic framework

Nonlinear free vibration analysis of elastically supported carbon nanotube-reinforced composite beam with the thermal environment in non-deterministic framework

Nonlocal modeling of a Carbon Nanotube actuated by an electrostatic force

Vibration characteristics of functionally graded carbon nanotube reinforced composite rectangular plates on Pasternak foundation with arbitrary boundary conditions and internal line supports

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