A unified formulation for free vibration of laminated plate through Jacobi-Ritz method

Qin, Bin; Zhong, Rui; Wu, Qiangyun; Wang, Tiantian; Wang, Qingshan

doi:10.1016/j.tws.2019.106354

Cited by 58 publications

(9 citation statements)

References 47 publications

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“…Because compared with directly building the displacement function of the whole structure, the displacement function only needs the low order polynomials for the segment structure. Here, the Jacobi orthogonal polynomials are applied to construct displacement functions [32][33][34][35][36], which can be expressed as…”

Section: Solution Process Of Laminated Annular/circular Platementioning

confidence: 99%

Vibration Characteristics Analysis of Composite Laminated Annular/Circular Plate Using High‐Order Shear Deformation Theory

Jin¹,

Ma²,

Zhang

et al. 2021

Shock and Vibration

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In this paper, the free vibration behaviors of composite laminated annular and circular plates under complex elastic boundary constraints are investigated. Firstly, Reddy’s high-order shear deformation theory (HSDT) and Jacobi polynomial method are effectively combined to establish the unified vibration analysis model of composite laminated annular and circular plates. Secondly, the simulation of complex elastic boundary and coupling boundary is realized by using artificial virtual spring technology. Then, the energy equation of the composite laminated plate is established by using Rayleigh–Ritz energy technology. Finally, the free vibration solution equation of the laminated plate is obtained through the Hamilton differential principle. The fast and uniform convergence of this method and the accuracy of the calculated results are verified by numerical examples and the model experimental method. On this basis, the parameterization study is conducted, and the effects of material parameters, geometric parameters, spring stiffness values, and lamination scheme on the vibration characteristics of the annular or circular plate are fully discussed, which can provide a theoretical basis for future research.

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Section: Solution Process Of Laminated Annular/circular Platementioning

confidence: 99%

Vibration Characteristics Analysis of Composite Laminated Annular/Circular Plate Using High‐Order Shear Deformation Theory

Jin¹,

Ma²,

Zhang

et al. 2021

Shock and Vibration

Self Cite

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“…A series of unknown coefficient is solved by bringing formal parameters into the governing equations. In this article, on the basis of the HSDT, a Jacobi-Ritz method combined with an artificial spring strategy (Qu et al, 2013; Qin et al, 2019b) and a Newmark method is presented, which is newly applied for solving both free and forced vibration problems of FGP annular and circular plates. The differences of the present methodology can be summarized as first, the HSDT is newly combined with the Jacobi–Ritz method in this paper.…”

Section: Introductionmentioning

confidence: 99%

A unified Jacobi–Ritz approach for the FGP annular plate with arbitrary boundary conditions based on a higher-order shear deformation theory

Zhao

Qin

Wang

et al. 2022

Journal of Vibration and Control

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In this paper, a unified method for free and forced vibration of functionally graded porous annular and circular plate is proposed, incorporating the Jacobi–Ritz method and the higher-order shear deformation theory. In order to improve the accuracy of calculation, the segment strategy is adopted. Meanwhile, the artificial spring is used to express the connection between each truncated plates and arbitrary boundary conditions. The convergency study and validation are implemented, and parametric study of both free and transient forced vibration are conducted. The present method shows a fast convergence property and high accuracy for thick plate. It has been found that boundary conditions are the dominant influencing factor of the central deflection of functionally graded porous annular plate, and the porous material with vertical gradient change in the plate leads to a better impedance effect than the uniformly distributed porous material.

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“…In order to overcome this defect and to obtain more accurate natural frequencies, FSDT was introduced considering the transverse shear deformations by applying the shear correction factor [11][12][13][14][15][16][17][18][19]. Qin et al [20] constructed the theoretical models in the framework of FSDT and introduced the multi-segment segmentation strategy to perform free vibration analysis of composite laminated rectangular plates according to arbitrary boundary conditions. Civalek et al [21,22] conducted studies on free vibration and buckling behavior of carbon nanotube (CNT)-reinforced cross-ply laminated composite and functionally graded plates based on FSDT.…”

Section: Introductionmentioning

confidence: 99%

A novel meshfree method for three-dimensional natural frequency analysis of thick laminated conical, cylindrical shells and annular plates

Kwak¹,

Kim²,

An³

et al. 2021

Phys. Scr.

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In this paper, a novel meshfree approach for three-dimensional free vibration analysis of thick laminated composite conical, cylindrical shells and annular plates is presented. The theoretical model for free vibration analysis of thick shells and plates is formulated by applying the three-dimensional theory of elasticity, and all displacement components are approximated by a novel meshfree Tchebychev-point interpolation method (TPIM) shape function using Tchebychev polynomials as a basis. After deriving the governing equations and boundary conditions for individual layers of the laminated shell, the governing equations and boundary conditions of the entire system are derived by combining them according to the order of layers. The boundary and combination conditions are generalized by introducing the artificial spring technique, and the type of conditions is selected by the spring stiffness values. The accuracy and reliability of the proposed method are verified by comparison with the results of literatures and finite element software ABAQUS. The free vibration characteristics such as the natural frequency and mode shape of laminated conical, cylindrical shells and annular plates under different boundary conditions are presented through some numerical examples.

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A unified formulation for free vibration of laminated plate through Jacobi-Ritz method

Cited by 58 publications

References 47 publications

Vibration Characteristics Analysis of Composite Laminated Annular/Circular Plate Using High‐Order Shear Deformation Theory

Vibration Characteristics Analysis of Composite Laminated Annular/Circular Plate Using High‐Order Shear Deformation Theory

A unified Jacobi–Ritz approach for the FGP annular plate with arbitrary boundary conditions based on a higher-order shear deformation theory

A novel meshfree method for three-dimensional natural frequency analysis of thick laminated conical, cylindrical shells and annular plates

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