Application of Haar wavelet discretization method for free vibration analysis of inversely coupled composite laminated shells

Kim, Kwanghun; Kim, Changrok; An, Kwangil; Kwak, Songhun; Ri, Kumchol; Ri, Kumsun

doi:10.1016/j.ijmecsci.2021.106549

Cited by 21 publications

(7 citation statements)

References 71 publications

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“…The fundamental theories of Haar wavelet have been reported in many literatures. [71][72][73][74][75][76][77][78][79] Therefore, in this work, its explanation is ignored. The Haar wavelet series is adopted to discretize the derivatives in governing equations of the system including boundary and connective conditions.…”

Section: Discretization By Haar Wavelet Functionmentioning

confidence: 99%

“…Some researchers studied the static and dynamic behaviors of various structures like beams, [66][67][68] plates, [69][70][71] and shells [71][72][73][74][75][76][77] by using the Haar wavelet. Recently, Kim et al [78][79][80][81] studied the free vibration of various composite material structures by using HWDM. Therefore, in this paper, FSDT and HWDM are applied to analyze the free vibrations of multi-stepped FG curved beams with generalized boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Free vibration analysis of a multi-stepped functionally graded curved beam with general boundary conditions

Kim¹,

Kwak²,

Jang

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this paper, a Haar wavelet discretization method (HWDM) for analyzing the free vibration of the multi-stepped functionally graded (FG) curved beam with general boundary conditions is presented. It is assumed that the material properties of the beam change continuously in the thickness direction according to the distribution characteristics of the material determined by four parameters. The individual steps of the multi-stepped functionally graded curved beam are combined by a continuous condition. For generalization of boundary conditions, the artificial elastic spring technique is introduced. The displacement fields are determined by the first-order shear deformation theory (FSDT) and the motion equation is obtained by using Hamilton’s principle. All displacement functions including boundary and continuity conditions are expressed in the form of a Haar wavelet series and its integral, and a characteristic equation discretized based on the Haar wavelet is obtained. The reliability and accuracy of the proposed method are confirmed through convergence and validation studies. The results indicate that this method has high accuracy and reliability, also a higher convergence rate in attaining the frequencies of the multi-stepped FG curved beam. Then, the frequency parameters and mode types of the multi-stepped FG curved beam obtained by the proposed method are given with numerical examples. These new numerical results can be used as benchmark data for research in this field.

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Section: Discretization By Haar Wavelet Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of a multi-stepped functionally graded curved beam with general boundary conditions

Kim¹,

Kwak²,

Jang

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the current study, Haar wavelet series are employed for the discretization of the derivatives in governing the equations of the whole system, including boundary conditions. e basic theories of Haar wavelet have been introduced in Xie's studies [4-6, 9, 11, 71] and author's studies [67,68,[72][73][74][75]. erefore, in this paper, the explanation for Haar wavelet is downplayed.…”

Section: Implementation Of the Hwdmmentioning

confidence: 99%

Free Vibration Analysis of Cross-Ply Laminated Conical Shell, Cylindrical Shell, and Annular Plate with Variable Thickness Using the Haar Wavelet Discretization Method

Kim¹,

Kim²,

Kim³

et al. 2022

Shock and Vibration

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This paper presents a unified solution method to investigate the free vibration behaviors of a laminated composite conical shell, a cylindrical shell, and an annular plate with variable thickness and arbitrary boundary conditions using the Haar wavelet discretization method (HWDM). Theoretical formulation is established based on the first-order shear deformation theory (FSDT), and displacement components are extended to the Haar wavelet series in the axis direction and trigonometric series in the circumferential direction. The constants generated by the integration process are disposed by boundary conditions, and thus the equations of the motion of the total system, including the boundary condition, are transformed into algebraic equations. Then, the natural frequencies of the laminated composite structures are directly obtained by solving these algebraic equations. The stability and accuracy of the present method are verified through convergence and validation studies. The effects of some material properties and geometric parameters on the free vibration of laminated composite shells are discussed and some related mode shapes are given. Some new results for laminated composite conical shell, cylindrical shell, and annular plate with variable thickness and arbitrary boundary conditions are presented, which may serve as benchmark solutions.

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“…In current study, Haar wavelet series are employed for discretization of the derivatives in governing equations of whole system including boundary conditions. The basic theories of Haar wavelet have been introduced in Xie's studies [52][53][54][55][56] and author's studies [57][58][59][60]. Therefore, in this paper, the explanation for Haar wavelet is downplayed.…”

Section: Implementation Of the Hwdmmentioning

confidence: 99%

“…The Haar wavelet method has been proven to be an effective tool for solving various problems, such as differential and integral equations [35][36][37][38][39][40][41][42][43], biharmonic equations and Poisson equations. In addition, the Haar wavelet has been also proven to be an effective tool for solving the static and dynamic problems of various structures, such as beams [44][45][46][47][48], plates [49][50][51] and shells [51][52][53][54][55][56][57][58][59][60]. Therefore, in this paper, the Haar wavelet discretization method, whose effectiveness has been verified in the vibration analysis of various laminated composite shell structures, is selected to investigate the free vibration characteristics of laminated composite conical, cylindrical and annular plate.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of laminated composite conical, cylindrical shell and annular plate with variable thickness and general boundary conditions

Kim

Kwak

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

This paper presents a unified solution method to investigate the free vibration behaviors of laminated composite conical shell, cylindrical shell and annular plate with variable thickness and arbitrary boundary conditions using the Haar wavelet discretization method (HWDM). Theoretical formulation is established based on the first order shear deformation theory(FSDT) and displacement components are extended Haar wavelet series in the axis direction and trigonometric series in the circumferential direction. The constants generating by the integrating process are disposed by boundary conditions, and thus the equations of motion of total system including the boundary condition are transformed into an algebraic equations. Then natural frequencies of the laminated composite structures are directly obtained by solving these algebraic equations. Stability and accuracy of the present method are verified through convergence and validation studies. Effects of some material properties and geometric parameters on the free vibration of laminated composite shells are discussed and some related mode shapes are given. Some new results for laminated composite conical shell, cylindrical shell and annular plate with variable thickness and arbitrary boundary conditions are presented, which may serve as benchmark solutions.

show abstract

Application of Haar wavelet discretization method for free vibration analysis of inversely coupled composite laminated shells

Cited by 21 publications

References 71 publications

Free vibration analysis of a multi-stepped functionally graded curved beam with general boundary conditions

Free vibration analysis of a multi-stepped functionally graded curved beam with general boundary conditions

Free Vibration Analysis of Cross-Ply Laminated Conical Shell, Cylindrical Shell, and Annular Plate with Variable Thickness Using the Haar Wavelet Discretization Method

Free vibration analysis of laminated composite conical, cylindrical shell and annular plate with variable thickness and general boundary conditions

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