Three-dimensional vibration analysis of circular and annular plates via the Chebyshev–Ritz method

Zhou, Ding; Au, Ftk; Cheung, Y.K.; Lo, S.H.

doi:10.1016/s0020-7683(03)00114-8

Cited by 119 publications

(59 citation statements)

References 14 publications

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“…There have been a number of investigations of the free vibration of homogeneous isotropic circular and annular plates such as Han and Liew (1999), Haterbouch and Benamar (2005), Liew et al (1997), Liew and Yang (1999), Liew and Yang (2000), Selmane and Lakis (1999) and Zhou et al (2003). There are works employing solutions using differential quadrature and generalized differential quadrature methods for the study of this class of problems and so also a few finite element solutions for the analysis of laminated plates and shells such as Han and Liew (1997), Lin and Tseng (1998), Ding and Xu (2000), Liew and Liu (2000), Wu et al (2002), Tornabene et al (2009) and Hosseini-Hashemi et al (2010).…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of axisymmetric laminated composite circular and annular plates using Chebyshev collocation

Powmya

Narasimhan

2015

Int J Adv Struct Eng

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Solutions, based on principle of collocating the equations of motion at Chebyshev zeroes, are presented for the free vibration analysis of laminated, polar orthotropic, circular and annular plates. The analysis is restricted to axisymmetric free vibration of the plates and employs firstorder shear deformation theory for the displacement field, in terms of midplane displacements, u, a and w. The eigenvalue problem is defined in terms of three equations of motion in terms of the radial co-ordinate r, the radial variation of the displacements being represented in polynomial series, with appropriate boundary conditions. Numerical results are presented to show the validity and accuracy of the proposed method. Results of parametric studies for laminated polar orthotropic circular and annular plates with different boundary conditions, orthotropic ratios, lamination sequences, number of layers and shear deformation are also presented.

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Section: Introductionmentioning

confidence: 99%

Free vibration analysis of axisymmetric laminated composite circular and annular plates using Chebyshev collocation

Powmya

Narasimhan

2015

Int J Adv Struct Eng

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“…Technically speaking, composites annular plates are widely used in industrial structural elements. There are large number of research papers and reviews on the free vibration analyses of isotropic annular plates [12][13][14][15][16][17][18][19] . A few researchers have analyzed vibration and static behavior of nanocomposites plates [20][21][22][23] .…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional free vibration analysis of carbon nanotube reinforced composites annular plates

Zali¹,

Yazdian²,

Omidi³

2015

Orient. J. Chem

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The main objective of this research work was to investigate three-dimensional free vibration of thick annular plates which are composed of carbon nanotube (CNT) reinforced composites materials using the Chebyshev-Ritz method. In order to obtain precise results, a new form of the rule of mixtures including an exponential shape function, length efficiency parameter, orientation efficiency factor, and waviness parameter was applied for predicting the mechanical properties of CNT reinforced composites. Convergence of the Chebyshev-Ritz method was also checked. Numerical results are given and compared with the available literature and finite element method (FEM) analysis. Results obtained from the other well-known theories (such as: Micro-Mechanical, Halpin, etc.) are compared with the new form of the rule of mixtures results. Furthermore, the effects of CNT type, structures, diameter, shape factor, density, and volume fraction on the vibration behavior of the annular plates are graphically presented.

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“…The stability of parametric vibrations of circular plate subjected to in-plane forces was analyzed using the Liapunov method by Tylikowski and Frischmuth (2003). Zhou et al (2003) employed Chebyshev-Ritz method in three-dimensional free vibration analysis of circular and annular plates. They used a linear analysis with small strain assumption.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Electromechanical Stability of a Functionally Graded Circular Plate Integrated With Functionally Graded Piezoelectric Layers

Arefi

2015

Lat. Am. j. solids struct.

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This research develops nonlinear electromechanical stability of a circular functionally graded plate integrated with functionally graded piezoelectric layers under compressive radial force. Geometric nonlinearity is considered in the strain-displacement relation using Von-Karman relation. The structure is loaded under mechanical and electrical loads. Distribution of electric potential is considered along the radial and thickness direction. The top and bottom of both piezoelectric layers is short-circuited. The effect of various values of non homogenous index for both functionally graded (FG) and functionally graded piezoelectric (FGP) layers can be considered on the responses of the system. Furthermore, a comprehensive study for evaluation of geometric parameters can be performed on the critical loads of the structure.

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Three-dimensional vibration analysis of circular and annular plates via the Chebyshev–Ritz method

Cited by 119 publications

References 14 publications

Free vibration analysis of axisymmetric laminated composite circular and annular plates using Chebyshev collocation

Free vibration analysis of axisymmetric laminated composite circular and annular plates using Chebyshev collocation

Three-dimensional free vibration analysis of carbon nanotube reinforced composites annular plates

Nonlinear Electromechanical Stability of a Functionally Graded Circular Plate Integrated With Functionally Graded Piezoelectric Layers

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