Differential quadrature method for nonlinear vibration of orthotropic plates with finite deformation and transverse shear effect

Li, J.-J.; Chang-jun, Cheng

doi:10.1016/j.jsv.2004.01.016

Cited by 38 publications

(18 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From [24],the DQ formulation in matrix form for the partial derivative of a function F (X, Y ) (representing U , V and W ) in two-dimensional domain may be given as…”

Section: Solution Methodsmentioning

confidence: 99%

“…Further using the Hadamard and Kronecker products of matrices [12,13,24], the coupled nonlinear formulas can be converted into the explicit matrix forms as follows: It has to be explained that the boundary conditions (4) have been considered when the coefficients in (8) are calculated [13,24]. Thus, it is not necessary to consider the boundary conditions (4) for solving (8).…”

Section: Solution Methodsmentioning

confidence: 99%

“…Liew et al [22,23] applied a semi-analytical Galerkindifferential quadrature to analyze the post-buckling and the dynamic stability of FGM plates based on the higher-order shear deformation theory (HSDT). Li and Cheng [24] used the DQM to analyze the nonlinear vibration of orthotropic rectangular plates. More recently, based on FSDT, Malekzadeh et al [25][26][27][28] analyzed the large deformation of thin composite plates and moderately thick composite plates by the DQM.…”

Section: Introductionmentioning

confidence: 99%

“…In order to solve the problem, the differential quadrature method is applied to discretize the governing equations on the spatial domain, and a set of integro-differential equations with regard to the time are yielded. A technique similar to the method in [12,24] is further extended to realize the nonlinear computation. Then, the dynamic behaviors of viscoelastic plates are numerically computed and analyzed by introducing new variables on the time domain.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Differential quadrature method for analyzing nonlinear dynamic characteristics of viscoelastic plates with shear effects

Chang-jun

2009

Nonlinear Dyn

Self Cite

View full text Add to dashboard Cite

The integro-partial differential equations governing the dynamic behavior of viscoelastic plates taking account of higher-order shear effects and finite deformations are presented. From the matrix formulas of differential quadrature, the special matrix product and the domain decoupled technique presented in this work, the nonlinear governing equations are converted into an explicit matrix form in the spatial domain. The dynamic behaviors of viscoelastic plates are numerically analyzed by introducing new variables in the time domain. The methods in nonlinear dynamics are synthetically applied to reveal plenty and complex dynamical phenomena of viscoelastic plates. The numerical convergence and comparison studies are carried out to validate the present solutions. At the same time, the influences of load and material parameters on dynamic behaviors are investigated. One can see that the system will enter into the chaotic state with a paroxysm form or quasi-periodic bifurcation with changing of parameters.

show abstract

“…From [24],the DQ formulation in matrix form for the partial derivative of a function F (X, Y ) (representing U , V and W ) in two-dimensional domain may be given as…”

Section: Solution Methodsmentioning

confidence: 99%

Section: Solution Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Differential quadrature method for analyzing nonlinear dynamic characteristics of viscoelastic plates with shear effects

Chang-jun

2009

Nonlinear Dyn

Self Cite

View full text Add to dashboard Cite

show abstract

“…A bending analysis of thin/thick laminated plates with various boundary conditions based on first-order shear deformation theory was described in [Aghdam et al 2006]. The DQ method was used in [Li and Cheng 2005;Tornabene and Viola 2008] to solve for the vibration of plates and shells. In [Malekzadeh and Setoodeh 2007], large deformation of laminated plates on a nonlinear elastic foundation was analyzed by the DQ method.…”

Section: Introductionmentioning

confidence: 99%

Bending of laminated plates with mixed boundary conditions based on higher-order shear deformation theory

Yaghoubshahi

Rajaie

2010

JOMMS

View full text Add to dashboard Cite

The bending of laminated plates is considered using higher-order transverse shear deformation theory. The principle of virtual work is used to derive a new set of seven governing equations and corresponding boundary conditions. These equations, combined with eighteen relationships between the resultant stress and displacement components, compose a system of first-order partial differential equations that is solved by the generalized differential quadrature method. Numerical results for laminated plates with a variety of mixed boundary conditions are calculated using the proposed method, and good agreement is found with the corresponding solutions obtained using ANSYS.

show abstract

A Study of Thermally Induced Vibrations of Circular Plate of Nonuniform Thickness

Sarswat¹,

Bansal²,

Kumar³

et al. 2019

International Conference on Intelligent Computing and Smart Communication 2019

View full text Add to dashboard Cite

Differential quadrature method for nonlinear vibration of orthotropic plates with finite deformation and transverse shear effect

Cited by 38 publications

References 18 publications

Differential quadrature method for analyzing nonlinear dynamic characteristics of viscoelastic plates with shear effects

Differential quadrature method for analyzing nonlinear dynamic characteristics of viscoelastic plates with shear effects

Bending of laminated plates with mixed boundary conditions based on higher-order shear deformation theory

A Study of Thermally Induced Vibrations of Circular Plate of Nonuniform Thickness

Contact Info

Product

Resources

About