Torsional oscillation of rigid disk in infinite transversely isotropic elastic cylinder

2006 ◽  
Vol 27 (7) ◽  
pp. 911-917 ◽  
Author(s):  
Sakti Pada Barik ◽  
Mridula Kanoria ◽  
P. K. Chaudhuri
Keyword(s):  
Torsional Oscillation ◽  
Transversely Isotropic ◽  
Elastic Cylinder ◽  
Rigid Disk

A Circular Elastic Cylinder Under Extension

2011 ◽  
Vol 27 (3) ◽  
pp. 399-407 ◽  
Author(s):  
W.-D. Tseng ◽  
J.-Q. Tarn
Keyword(s):  
Transversely Isotropic ◽  
Elastic Cylinder ◽  
Axisymmetric Deformation ◽  
Axial Stiffness ◽  
Stress Distributions ◽  
End Effect ◽  
Rigorous Solution ◽  
Concentrated Load ◽  
End Conditions ◽  
Space Formalism

ABSTRACTAnalysis of deformation and stress field in a circular elastic cylinder under the extension is presented, with emphasis on the end effect. The problem is formulated on the basis of the state space formalism for axisymmetric deformation of transversely isotropic materials. A rigorous solution that satisfies the prescribed end conditions is determined by using symplectic eigenfunction expansion, thereby, the applicability of the Saint-Venant solution is examined. The results show that the end effect is significant but confined to a local region near the base of the cylinder where the end plane is perfectly bonded or subjected to a concentrated load. As the axial stiffness increases, the end effect on the stress state increases at the loaded end but decreases at the bonded end. The displacement and stress distributions across the section are uniform throughout the length of the cylinder except near the ends.

Axisymmetric Free Vibrations of a Transversely Isotropic Finite Cylindrical Rod

1988 ◽  
Vol 55 (4) ◽  
pp. 855-862 ◽  
Author(s):  
C. P. Lusher ◽  
W. N. Hardy
Keyword(s):  
Boundary Conditions ◽  
Elastic Constants ◽  
Transversely Isotropic ◽  
Acoustic Vibration ◽  
Elastic Cylinder ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Hexagonal Symmetry ◽  
Hexagonal System ◽  
Better Than

The frequencies of free vibration and mode shapes are calculated for axisymmetric modes of an elastic cylinder of finite length having hexagonal symmetry with the crystallographic c-axis coincident with the axis of the cylinder (a transversely isotropic finite cylindrical rod). A series solution is used which satisfies term-by-term the differential equations of linear elasticity and the boundary conditions on the shear stress; the boundary conditions on the normal stresses are satisfied by using an orthogonalization procedure. As an example, the method is applied to sapphire, with one of the six elastic constants (c14) taken to be zero. The other five elastic constants are those of the hexagonal system. The calculated acoustic vibration frequencies agree to better than 1 percent with measurements made on sapphire at room temperature, for a cylinder of half-height to radius ratio ∼ 1.

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