Effect of symmetrical boundary conditions on the vibration of thick hollow cylinders

Buchanan, George R.; Yii, C.B.Y.

doi:10.1016/s0003-682x(01)00048-2

Cited by 22 publications

(24 citation statements)

References 13 publications

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“…A finite element for axisymmetric elasticity is formulated directly in the cylindrical coordinates to study the vibration of hollow, isotropic, and homogeneous finite length cylinders and frequencies are computed for free-free end boundary conditions in the reference 19 and compared with the reference. 16 For solving the aforementioned problem using the graded finite element method developed here, we considered a thick hollow cylinder with freely supported end conditions in which the material distribution is uniform.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Free Vibration Analysis of Functionally Heterogeneous Hollow Cylinder Based on Three Dimensional Elasticity Theory

Asgari¹

2017

IJAV

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A two-dimensional functionally heterogeneous thick hollow cylinder with a finite length is considered and its natural modes and frequencies are determined. Since mode shapes of a thick cylinder are three-dimensional, even with axisymmetric conditions, three-dimensional theory of elasticity implemented for problem formulation. The axisymmetric conditions are assumed for the cylinder. The material properties of the two-dimensional functionally graded material (2D-FGM) cylinder are varied in the radial and axial directions with power law functions. Effects of volume fraction distribution on the different types of anti-symmetric mode shape configuration and vibrational behaviour of a simply supported cylinder are analyzed. Three-dimensional equations of motion are used and the eigen value problem is developed based on direct variational method. The study shows that the 2D-FGM cylinder exhibit interesting vibrational characteristics and mode shapes when the constituent volume fractions are varied.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Free Vibration Analysis of Functionally Heterogeneous Hollow Cylinder Based on Three Dimensional Elasticity Theory

Asgari¹

2017

IJAV

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“…A finite element model for axisymmetric elasticity is formulated directly in the cylindrical coordinates to study the vibration of hollow, isotropic and homogeneous finite length cylinders and frequencies are computed for free-free end boundary conditions in the reference [27] and compared with the reference [13]. For solving the mentioned problem by graded finite element method developed here, we consider a thick hollow cylinder with freely supported end conditions in which the material distribution is uniform.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…A solution that satisfies the circumferential displacement and defines a circular frequency is [27]:…”

Section: Governing Equationsmentioning

confidence: 99%

Two Dimensional Functionally Graded Material Finite Thick Hollow Cylinder Axisymmetric Vibration Mode Shapes Analysis Based on Exact Elasticity Theory

Asgari¹

2015

Journal of Theoretical and Applied Mechanics

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Abstract. A thick hollow cylinder with finite length made of twodimensional functionally graded material (2D-FGM) is considered and its natural modes are determined, based on great importance of mode shapes information in order to understand vibration behaviour of structures. Three dimensional theory of elasticity implemented for problem formulation, since mode shapes of a thick cylinder are three dimensional even with axisymmetric conditions. The axisymmetric conditions are assumed for the 2D-FGM cylinder. The material properties of the cylinder are varied in the radial and axial directions, with power law functions. Effects of volume fraction distribution on the different types of symmetric mode shapes configuration and vibration behaviour of a simply supported cylinder are analyzed. Three dimensional equations of motion are used and the eigen value problem is developed, based on direct variation method.

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“…An analysis for the cylindrical section was compared to previous studies for hollow cylinders [7] and was found to give satisfactory results.…”

Section: Finite Element Modelsmentioning

confidence: 92%

An Analysis of the Free Vibration of a Hermetic Capsule

Buchanan¹

2003

Journal of Sound and Vibration

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Effect of symmetrical boundary conditions on the vibration of thick hollow cylinders

Cited by 22 publications

References 13 publications

Free Vibration Analysis of Functionally Heterogeneous Hollow Cylinder Based on Three Dimensional Elasticity Theory

Free Vibration Analysis of Functionally Heterogeneous Hollow Cylinder Based on Three Dimensional Elasticity Theory

Two Dimensional Functionally Graded Material Finite Thick Hollow Cylinder Axisymmetric Vibration Mode Shapes Analysis Based on Exact Elasticity Theory

An Analysis of the Free Vibration of a Hermetic Capsule

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