Axisymmetric vibration of layered orthotropic spherical shells of variable thickness

1992 ◽  
Vol 45 (5-6) ◽  
pp. 893-900 ◽  
Author(s):  
B.P. Gautham ◽  
N. Ganesan
Keyword(s):  
Variable Thickness ◽  
Axisymmetric Vibration ◽  
Spherical Shells

Some Results on Axisymmetric Vibration of Spherical Shells of Variable Thickness

1990 ◽  
Vol 112 (4) ◽  
pp. 432-437 ◽  
Author(s):  
A. V. Singh ◽  
S. Mirza
Keyword(s):  
Variable Thickness ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Axisymmetric Vibration ◽  
Spherical Shells ◽  
Varying Thickness ◽  
Wide Range

Natural frequencies and mode shapes are presented for the free axisymmetric vibration of spherical shells with linearly varying thickness along the meridian. Clamped and hinged edges corresponding to opening angles 30, 45, 60 and 90 deg have been considered in this technical brief to cover a wide range from shallow to deep spherical shells. Variations in thickness are seen to have very pronounced effects on the frequencies and mode shapes.

Research on Axisymmetric Vibration of Gear with Stepped Variable Thickness

2011 ◽  
Vol 320 ◽  
pp. 269-274
Author(s):  
Yin Zhu She ◽  
Ming Lv ◽  
Shi Ying Wang
Keyword(s):  
Natural Frequency ◽  
Variable Thickness ◽  
Plate Theory ◽  
Great Influence ◽  
Special Kind ◽  
Structure Characteristic ◽  
Axisymmetric Vibration ◽  
Bending Vibration ◽  
Factors Affecting ◽  
Application Range

Ultrasonic gear honing is a kind of precision processing technology with great application prospect. The gear is a special kind of load in ultrasonic machining, and its vibration characteristic and natural frequency has great influence on processing frequency of the system. According to the structure characteristic of the gear with stepped variable thickness, its equations of axisymmetric bending vibration frequency were derived on the basis of the thick plate theory in this paper, and then the gear’s natural frequency is obtained which is in accordance with the results of FEM computation. Besides, the main factors affecting the calculation accuracy are analyzed with some examples in this paper The analysis shows that within the application range of Mindlin’s plate theory, the gears’ frequency obtained by the suggested method is accurate.

Axisymmetric Vibration of Rotating Annular Plate with Variable Thickness Subjected to Tensile Centrifugal Body Force

2017 ◽  
Vol 17 (09) ◽  
pp. 1750101 ◽  
Author(s):  
Jae-Hoon Kang
Keyword(s):  
Variable Thickness ◽  
Body Force ◽  
Annular Plate ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Angular Speed ◽  
Plane Elasticity ◽  
Outer Radius ◽  
Axisymmetric Vibration ◽  
Rotating Annular Plate

This paper is concerned with the axisymmetric free vibration analysis of a rotating annular plate with variable thickness by using the Ritz method. The rotating plate has a constant angular speed and subjected to a tensile centrifugal body force. The annular plate is fixed at the inner edge and free at the outer edge. Exact stresses, strains, and radial displacement of the rotating annular plate are obtained via plane elasticity. Presented herein are the natural frequencies and modes shapes for the rotating, nonuniform annular plate with various angular speeds and different ratios of the inner radius to the outer radius.

Some Remarks on Spherical Shells

1965 ◽  
Vol 32 (1) ◽  
pp. 121-128
Author(s):  
C. N. DeSilva ◽  
H. Cohen
Keyword(s):  
Asymptotic Solution ◽  
Spherical Shell ◽  
Variable Thickness ◽  
Transverse Shear ◽  
Correction Term ◽  
Transverse Shear Deformation ◽  
Governing Equations ◽  
Spherical Shells ◽  
Annular Disk ◽  
Thickness Function

The present paper treats the deformation of a spherical shell within the framework of a linear bending theory which includes the effect of transverse-shear deformation. A two-term asymptotic solution of the governing equations is obtained which embraces all terms of an order retained in the formulation of the theory. The solution is valid within a physically important domain of the shell and reduces to the previously known one-term asymptotic solution of the classical bending theory. The problem of variable thickness is also discussed. The behavior of the thickness function may be such as to require in the solution a correction term which may contribute significantly to the deformation. This solution is applied to a treatment of the deformation of a rotating, completely closed spherical shell stiffened by an annular disk located normal to the axis of the spin.

Stress–strain state of nonthin orthotropic spherical shells of variable thickness

2012 ◽  
Vol 48 (1) ◽  
pp. 80-93 ◽  
Author(s):  
A. Ya. Grigorenko ◽  
O. V. Vovkodav ◽  
S. N. Yaremchenko
Keyword(s):  
Variable Thickness ◽  
Strain State ◽  
Stress Strain ◽  
Spherical Shells ◽  
Stress Strain State

Nonlinear Axisymmetric Free Vibration Analysis of Liquid-Filled Spherical Shell With Volume Constraint

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
W. Jiammeepreecha ◽  
S. Chucheepsakul
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Internal Pressure ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Axisymmetric Vibration ◽  
Volume Constraint ◽  
Constraint Condition ◽  
Spherical Shells

Nonlinear axisymmetric free vibration analysis of liquid-filled spherical shells with volume constraint condition using membrane theory is presented in this paper. The energy functional of the shell and contained liquid can be expressed based on the principle of virtual work using surface fundamental form and is written in the appropriate forms. Natural frequencies and the corresponding mode shapes for specified axisymmetric vibration amplitude of liquid-filled spherical shells can be calculated by finite element method (FEM). A nonlinear numerical solution can be obtained by the modified direct iteration technique. The results indicate that the Lagrange multiplier is a parameter for adapting the internal pressure in order to sustain the shell in equilibrium state for each mode of vibration with the volume constraint condition. The axisymmetric mode shapes of the liquid-filled spherical shells under volume constraint condition were found to be in close agreement with those in existing literature for an empty spherical shell. Finally, the effects of support condition, thickness, initial internal pressure, bulk modulus of internal liquid, and elastic modulus on the nonlinear axisymmetric free vibration and change of pressure of the liquid-filled spherical shells with volume constraint condition were demonstrated. The parametric studies showed that the change of pressure has a major impact on the fundamental vibration mode when compared with the higher vibration modes.

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