A solution method for free vibrration analysis of the elastically joined functionally graded shells

An, Kwangil; Jon, Yongsu; Kim, Kwanghun; Kim, Sok; Kim, Cholsik

doi:10.1140/epjp/s13360-021-01748-7

Cited by 7 publications

(3 citation statements)

References 70 publications

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“…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.

show abstract

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…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

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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

Free Vibration Analysis of Laminated Composite Spherical Shell with Variable Thickness and Different Boundary Conditions

Kim¹,

Kwak³

et al. 2021

J. Vib. Eng. Technol.

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A solution method for free vibrration analysis of the elastically joined functionally graded shells

Cited by 7 publications

References 70 publications

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 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

Free Vibration Analysis of Laminated Composite Spherical Shell with Variable Thickness and Different Boundary Conditions

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