Three-dimensional transient analysis of functionally graded material annular sector plate under various boundary conditions

Liang, Xu; Kou, Hai‐lei; Wang, Lizhong; Palmer, Andrew; Wang, Zhengyu; Li, Guohua

doi:10.1016/j.compstruct.2015.05.066

Cited by 25 publications

(9 citation statements)

References 48 publications

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“…In order to convert the derivative term with respect to the x coordinate to polynomials, the differential quadrature method (DQM) is employed to discretize the fundamental equations. Considering a continuous function f(x), the nth order partial derivative with respect to x at a given point x = x i can be approximated by a linear weighted sum of function values at all the sample points in the domain of x, that is (Liang et al, 2015):…”

Section: Differential Quadrature Methods (Dqm)mentioning

confidence: 99%

Semi-analytical solution for dynamic behavior of a fluid-conveying pipe with different boundary conditions

et al. 2018

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This paper analyzes the dynamic behavior of a fluid-conveying pipe with different pipe end boundary conditions. The pipe is considered to be an Euler-Bernoulli beam, and a motion equation for the pipe is derived using Hamilton's principle. A semi-analytical method, which includes the differential quadrature method (DQM) and the Laplace transform and its inverse, is used to obtain a model for the dynamic behavior of the pipe. The use of DQM provides a solution in terms of pipe length whereas use of the Laplace transform and its inverse produce a solution in terms of time. An examination of the results of sampling pipe displacement at different numbers of sample points along the pipe length shows that the method we developed has a fast convergence rate. The frequency and critical velocity of the fluid-conveying pipe derived by DQM are exactly the same as the exact solution. The numerical results given by the model match well with the result obtained using the Galerkin method. The effect on pipe displacement of the pipe end boundary conditions is investigated, and it increases with an increase in the edge degrees of freedom. The results obtained in this paper can serve as benchmark data in further research.

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Section: Differential Quadrature Methods (Dqm)mentioning

confidence: 99%

Semi-analytical solution for dynamic behavior of a fluid-conveying pipe with different boundary conditions

et al. 2018

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“…. , N x ; f (ε j ) = f j ; p j (ε) are the Lagrange interpolation polynomials, and A r ij is the weight coefficient of the r th derivative defined by [41]:…”

Section: Differential Quadrature Methodsmentioning

confidence: 99%

A Numerical Method for Flexural Vibration Band Gaps in A Phononic Crystal Beam with Locally Resonant Oscillators

et al. 2019

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The differential quadrature method has been developed to calculate the elastic band gaps from the Bragg reflection mechanism in periodic structures efficiently and accurately. However, there have been no reports that this method has been successfully used to calculate the band gaps of locally resonant structures. This is because, in the process of using this method to calculate the band gaps of locally resonant structures, the non-linear term of frequency exists in the matrix equation, which makes it impossible to solve the dispersion relationship by using the conventional matrix-partitioning method. Hence, an accurate and efficient numerical method is proposed to calculate the flexural band gap of a locally resonant beam, with the aim of improving the calculation accuracy and computational efficiency. The proposed method is based on the differential quadrature method, an unconventional matrix-partitioning method, and a variable substitution method. A convergence study and validation indicate that the method has a fast convergence rate and good accuracy. In addition, compared with the plane wave expansion method and the finite element method, the present method demonstrates high accuracy and computational efficiency. Moreover, the parametric analysis shows that the width of the 1st band gap can be widened by increasing the mass ratio or the stiffness ratio or decreasing the lattice constant. One can decrease the lower edge of the 1st band gap by increasing the mass ratio or decreasing the stiffness ratio. The band gap frequency range calculated by the Timoshenko beam theory is lower than that calculated by the Euler-Bernoulli beam theory. The research results in this paper may provide a reference for the vibration reduction of beams in mechanical or civil engineering fields.

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“…At the outer and inner surfaces, the boundaries equations (31) and (32) are applied into equation (38) f…”

Section: Semi-analytical Solutionmentioning

confidence: 99%

Three-dimensional semi-analytical solutions for the transient response of functionally graded material cylindrical panels with various boundary conditions

Liang

Deng

Jiang

et al. 2019

Journal of Low Frequency Noise, Vibration and Active Control

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In this paper, a 3D semi-analytical method is proposed by introducing the Durbin's Laplace transform, as well as its numerical inversion method, state space approach and differential quadrature method to analyse the transient behaviour of functionally graded material cylindrical panels. Moreover, to investigate the effectiveness of the proposed semianalytical solution, four boundary conditions are used to undertake the analyses. Comparing the proposed approach with other theoretical methods from the literatures, we see better agreements in the natural frequencies. Besides, the semi-analytical solution acquires nearly the same transient response as those obtained by ANSYS. Convergence studies indicate that the proposed method has a quick convergence rate with growing sample point numbers along the length direction, so do layer numbers increase along the radial direction. The effects of thickness/outer radius ratio, length/outer radius ratio and functionally graded indexes are also studied. When carbon nanotube is added to functionally graded material cylindrical panel, the composite structures have been reinforced greatly. The proposed 3D semi-analytical method has high accuracy for the analysis of composite structures. This study can serve as a foundation for solving more complicated environments such as fluid-structure interaction of flexible pipe or thermal effect analysis of functionally graded material in aerospace field.

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Three-dimensional transient analysis of functionally graded material annular sector plate under various boundary conditions

Cited by 25 publications

References 48 publications

Semi-analytical solution for dynamic behavior of a fluid-conveying pipe with different boundary conditions

Semi-analytical solution for dynamic behavior of a fluid-conveying pipe with different boundary conditions

A Numerical Method for Flexural Vibration Band Gaps in A Phononic Crystal Beam with Locally Resonant Oscillators

Three-dimensional semi-analytical solutions for the transient response of functionally graded material cylindrical panels with various boundary conditions

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