Free vibration analysis of elastically connected composite laminated double-plate system with arbitrary boundary conditions by using meshfree method

Kim, Kwanghun; Kwak, Songhun; Jang, Paeksan; Sok, Myongkuk; Jon, Sunjong; Ri, Kumchol

doi:10.1063/5.0040270

Cited by 22 publications

(4 citation statements)

References 71 publications

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“…Cao et al, 14 introduced a multilayer moving plate method for the dynamic analysis of viscoelastically connected infinitely long double-plate systems subjected to moving loads. Kim et al, 15 studied the free vibration of a composite laminated double-plate system using the mesh-free method, wherein all of the displacement functions, including the boundary conditions, are approximated by the mesh-free shape function. Zhang et al, 16 investigated the free vibration of a laminated composite double-plate system based on the improved Fourier series methods.…”

Section: Introductionmentioning

confidence: 99%

Symplectic analytical solution for forced vibration of a multilayer plate system

Ma,

Cheng,

Wang

2023

Journal of Low Frequency Noise, Vibration and Active Control

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The classical laminate and lattice sandwich plate structure can be simplified into a multilayer plate system, wherein the plate components of the system are continuously joined along the transverse direction by elastic layers and can have different combinations of boundary conditions. A symplectic analytical wave propagation approach is developed for the forced vibration of a system of multiple elastically connected thin plates considering the Kirchhoff thin plate theory. The proposed method overcomes the limitation of the traditional analytical method, wherein the exact vibration field function only exists for a system with all edges of the plate components simply supported. First, the coupled partial differential equations governing the vibration of the multi-plate system are decoupled using a technique based on matrix theory; for decoupled equations, a general “vibration” state is innovatively introduced into the symplectic dual system. Next, the general “vibration” state can be analytically described in symplectic space by solving the symplectic eigenproblem and utilizing wave propagation theory. Finally, by using these analytical wave shapes and satisfying the physical boundary conditions of the system, the forced responses can be analytically calculated. In the numerical examples, the forced transverse vibrations of the double- and three-plate systems are investigated, and the cases with various combinations of boundary conditions are considered. The effectiveness of the present method is validated by comparing the present results with the results from the literature and those calculated using the finite element method. The influence of the elastic layer stiffness and number of plate components on the vibration is also investigated.

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Section: Introductionmentioning

confidence: 99%

Symplectic analytical solution for forced vibration of a multilayer plate system

Ma,

Cheng,

Wang

2023

Journal of Low Frequency Noise, Vibration and Active Control

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“…Therefore, the vibration analysis results of the moderately thick shell and plate using CPT are not very accurate. 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.…”

Section: Introductionmentioning

confidence: 99%

“…Meshfree method does not have a long history of development, but its idea is very unique and has good computational effect. So, it is increasingly attracting the attention of many scholars, and many studies are being conducted to analyze the static and dynamic characteristics of laminated shells and plates using it [40][41][42][43][44][45][46][47][48]. As with the other numerical solution methods, the meshfree shape function plays a very important role in ensuring the effectiveness of solution.…”

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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“…The FSDT is a theory to overcome the CPT's drawback. Many problems have been solved with the aid of FSDT [12][13][14][15][16][17][18][19][20][21]. The FSDT has also some deficiencies because the shear correction factor is not considered and the transverse shear strain is assumed to be constant in this theory.…”

Section: Introductionmentioning

confidence: 99%

A meshfree moving least squares-Tchebychev shape function approach for free vibration analysis of laminated composite arbitrary quadrilateral plates with hole

Kwak¹,

Kim²,

An³

et al. 2021

Phys. Scr.

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In this paper, a new meshfree moving least squares-Tchebychev (MLST) shape function is proposed to analyze the free vibration characteristics of laminated composite arbitrary quadrilateral plate with hole. The plate and hole have an arbitrary quadrilateral shape. The whole plate structure is separated into the segments with arbitrary quadrilateral shape by the domain decompose method, and these segments are modeled to a square plate through the coordinate mapping. The fourth order polynomial mapping approach is used as a mapping function for the coordinate mapping. The first-order shear deformation theory (FSDT) is adopted in theoretical formulation for the free vibration analysis of laminated composite arbitrary quadrilateral plate. The boundary and continuation conditions are generalized by the artificial spring technique. All the displacement functions containing the boundary and continuation conditions are expressed by the meshfree MLST shape function, on the base of this, the governing equation of arbitrary plate with hole are obtained. Thus, the natural frequency and mode shape of the laminated composite arbitrary quadrilateral plate with hole are obtained by solving the governing equation. The accuracy and reliability of the proposed method are verified by comparison with the results of literature and ABAQUS. Through numerical verification, it can be seen that the results of the proposed method are in good agreement with those of the literature and ABAQUS. The free vibration characteristics (i.e. natural frequency and mode shape) of the laminated composite arbitrary quadrilateral plate with arbitrary quadrilateral hole under different boundary conditions are proposed through the parameter research and some examples. RECEIVED

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Free vibration analysis of elastically connected composite laminated double-plate system with arbitrary boundary conditions by using meshfree method

Cited by 22 publications

References 71 publications

Symplectic analytical solution for forced vibration of a multilayer plate system

Symplectic analytical solution for forced vibration of a multilayer plate system

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

A meshfree moving least squares-Tchebychev shape function approach for free vibration analysis of laminated composite arbitrary quadrilateral plates with hole

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