Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment

Lei, Zhiwei; Liew, K.M.; Yu, Jilin

doi:10.1016/j.compstruct.2013.06.003

Cited by 244 publications

(70 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this example, the study is without regard to the internal line supports and foundation coefficients. In order to check the presented method, the numerical results reported by Liew et al using the element-free kp-Ritz method [27] and finite element method [9] on the basis of FSDT are also given in the above tables for comparison. From the comparison, we can see a consistent agreement of the results taken from the current method and reference data.…”

Section: Convergence and Comparison Studiesmentioning

confidence: 99%

“…Zhang et al [18] and Lei et al [19] respectively studied the free vibration characteristics of FG-CNT reinforced composite plates with elastically restrained edges and laminated plates with FG-CNT reinforced composite layers. Liew and his co-authors [20][21][22][23][24][25][26][27] employed the element-free kp-Ritz method to study the vibration characteristics of the FG-CNT reinforced composite plates, i.e. buckling of skew FG-CNT reinforced composite plates, post-buckling of FG-CNT reinforced composite plates subjected to in-plane compressive loads, linear stress analysis of FG-CNT reinforced composite plates and so on.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

View full text Add to dashboard Cite

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.

show abstract

Section: Convergence and Comparison Studiesmentioning

confidence: 99%

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

View full text Add to dashboard Cite

show abstract

“…It should be noted that in the case of free vibration ( 1,2,3) i Ni  are assumed to be zero. The arrays of matrix ij S are obtained from…”

Section: Motion Equations Based On Hamilton's Principlementioning

confidence: 99%

“…They have studied on the influences of the volume fractions of carbon nanotubes and the edge-to-thickness ratios on the bending responses, natural frequencies and mode shapes of the plates. Also, Lei et al [3] have done similar work before, but they used the element free kP-Ritz method in thermal environment. Bending behavior of functionally graded carbon nanotube reinforced composite (FG-CNTRC) plate embedded in thin piezoelectric layers subjected to mechanical uniform load is investigated by Alibeigloo [4].…”

Section: Introductionmentioning

confidence: 99%

Vibration Characteristics of Axially Moving Titanium- Polymer Nanocomposite Faced Sandwich Plate Under Initial Tension

Arani

Haghparast²,

Zarei³

2017

International Journal of Engineering &Amp; Applied Sciences

View full text Add to dashboard Cite

show abstract

“…Alibeigloo [7] carried out a static analysis of a CNT-reinforced composite rectangular host plate attached to thin piezoelectric layers and subjected to thermal loading and/or an electric field. Lei et al [8] employed the element-free kernel particle Ritz (kp-Ritz) method to study the free vibration of CNT-reinforced functionally graded composite rectangular…”

Section: Introductionmentioning

confidence: 99%

Geometrically nonlinear large deformation of CNT-reinforced composite plates with internal column supports

Zhang

2017

Journal of Modeling in Mechanics and Materials

View full text Add to dashboard Cite

Abstract:The geometrical nonlinear analysis of internally supported nanocomposite plates subjected to a uniformly distributed load is carried out. This study investigates the effects of internal point/column supports on the large deformation bending of nanocomposite plates reinforced by carbon nanotubes (CNTs) with different types of distributions, namely, uniform and two kinds of functionally graded distributions through the thickness of the plates. Two-dimensional displacement field of the plate is approximated by a set of Improved Moving Least Squares (IMLS) functions. The arc-length iterative algorithm with the modified Newton method is employed to obtain the nonlinear response of nanocomposite plates. Convergence studies indicate the validity and effectiveness of the element-free IMLS-Ritz method. The effects of plate thickness-to-width ratio, volume fraction ratio, and plate aspect ratio on the large deformation behavior of nanocomposite plates under various boundary conditions are examined. To the best of the authors' knowledge, the problem has not been attempted in the open literature.

show abstract

Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment

Cited by 244 publications

References 59 publications

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

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

Vibration Characteristics of Axially Moving Titanium- Polymer Nanocomposite Faced Sandwich Plate Under Initial Tension

Geometrically nonlinear large deformation of CNT-reinforced composite plates with internal column supports

Contact Info

Product

Resources

About