Dynamic stiffness vibration analysis of thick spherical shell segments with variable thickness

Efraim, Elia; Eisenberger, Moshe

doi:10.2140/jomms.2010.5.821

Cited by 22 publications

(4 citation statements)

References 11 publications

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“…Based on the classical Donnell's and Love's shell theories, Taati et al [38] investigated the free vibration characteristics of thin cylindrical shells with variable thickness and a constant angular velocity. Efraim and Eisenberger [39] obtained the free vibration frequencies and mode shapes of thick spherical shell segments with variable thickness and different boundary conditions using the dynamic stiffness method. Zheng et al [40] applied the energy method based on the Donnell-Mushtari shell theory to investigate the vibration characteristics of the cylindrical shell with arbitrary variable thickness and general boundary conditions.…”

Section: Introductionmentioning

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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Section: Introductionmentioning

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

View full text Add to dashboard Cite

show abstract

“…Based on the classical Donnell's and Love's shell theories, Taati et al [18] investigate the free vibration characteristics of thin cylindrical shells with variable thickness and a constant angular velocity. Efraim and Eisenberger [19] obtained the free vibration frequencies and mode shapes of thick spherical shell segments with variable thickness and different boundary conditions using a dynamic stiffness method. Zheng et al [20] applied energy method based on Donnell-Mushtari shell theory to investigate the vibration characteristics of cylindrical shell with arbitrary variable thickness and general boundary conditions.…”

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

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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.

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“…The works by Kang and Leissa [85,86] and by Leissa and Kang [87] represented a great contribution to this topic for the results given on thick spherical and paraboloidal shells of revolution with variable thickness obtained by a three-dimensional analysis. The dynamic stiffness method was employed by Efraim and Eisenberger [88] to compute the natural frequencies of thick spherical shell panels with variable thickness for various boundary restraints, taking into account both the effects of transverse shear stresses and rotary inertia. Finally, Jiang and Redekop [89] studied the free vibrations of orthotropic toroidal shells described by the Sanders-Budiansky equations by means of a semi-analytical differential quadrature method.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Investigation on the Natural Frequencies of FGM Sandwich Shells with Variable Thickness by the Local Generalized Differential Quadrature Method

et al. 2017

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Abstract:The main aim of the present paper is to solve numerically the free vibration problem of sandwich shell structures with variable thickness and made of Functionally Graded Materials (FGMs). Several Higher-order Shear Deformation Theories (HSDTs), defined by a unified formulation, are employed in the study. The FGM structures are characterized by variable mechanical properties due to the through-the-thickness variation of the volume fraction distribution of the two constituents and the arbitrary thickness profile. A four-parameter power law expression is introduced to describe the FGMs, whereas general relations are used to define the thickness variation, which can affect both the principal coordinates of the shell reference domain. A local scheme of the Generalized Differential Quadrature (GDQ) method is employed as numerical tool. The natural frequencies are obtained varying the exponent of the volume fraction distributions using higher-order theories based on a unified formulation. The structural models considered are two-dimensional and require less degrees of freedom when compared to the corresponding three-dimensional finite element (FE) models, which require a huge number of elements to describe the same geometries accurately. A comparison of the present results with the FE solutions is carried out for the isotropic cases only, whereas the numerical results available in the literature are used to prove the validity as well as accuracy of the current approach in dealing with FGM structures characterized by a variable thickness profile.

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Dynamic stiffness vibration analysis of thick spherical shell segments with variable thickness

Cited by 22 publications

References 11 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

A Numerical Investigation on the Natural Frequencies of FGM Sandwich Shells with Variable Thickness by the Local Generalized Differential Quadrature Method

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