R-Function Theory method for free vibration of slip clamped trapezoidal shallow spherical shell

2015 ◽  
pp. 947-949
Author(s):  
Shanqing Li ◽  
Hong Yuan
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Function Theory ◽  
Shallow Spherical Shell ◽  
Theory Method

Large Amplitude Free Vibration of Shallow Spherical Shell on a Pasternak Foundation

1993 ◽  
Vol 115 (1) ◽  
pp. 70-74 ◽  
Author(s):  
D. N. Paliwal ◽  
V. Bhalla
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Large Amplitude ◽  
Free Vibrations ◽  
Numerical Results ◽  
Shallow Spherical Shell ◽  
Pasternak Foundation ◽  
New Approach ◽  
Foundation Parameters ◽  
Clamped Edges

Large amplitude free vibrations of a clamped shallow spherical shell on a Pasternak foundation are studied using a new approach by Banerjee, Datta, and Sinharay. Numerical results are obtained for movable as well as immovable clamped edges. The effects of geometric, material, and foundation parameters on relation between nondimensional frequency and amplitude have been investigated and plotted.

Free Vibration of Shallow-Spherical Shell

2014 ◽  
Vol 578-579 ◽  
pp. 890-894
Author(s):  
Xian Qin Hou
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Spherical Shell ◽  
Solution Method ◽  
Shallow Spherical Shell ◽  
Frequency Curve ◽  
Third Order ◽  
Practical Solution ◽  
Clamped Edge

Shallow spherical shell is one of the structure shapes and is adopted extensively in engineering. Based on the exact solution of free vibration of the shallow-spherical shell, the frequency equations of the shallow spherical shell with clamped edge are derived and calculated numerically. Then the first third-order frequency curve and modal curve and solved. Comparing these with the results of the exact-solution method, the range of of the shallow-spherical shell when calculated by use of practical-solution method can be derived.

The Free Vibrations of a Spinning Centrally Clamped Shallow Spherical Shell

1971 ◽  
Vol 38 (3) ◽  
pp. 601-607 ◽  
Author(s):  
R. J. Beckemeyer ◽  
W. Eversman
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Flexural Rigidity ◽  
Polar Axis ◽  
Free Vibrations ◽  
Shallow Spherical Shell ◽  
Radius Of Curvature ◽  
Difficult Case ◽  
Equilibrium Equations ◽  
Continuous Transition

The results of a numerical analysis of the free-vibration characteristics of a thin shallow spherical shell spinning about its polar axis are presented. The shell is fully clamped by a central hub. The static equilibrium equations are formulated allowing for finite rotations. The free-vibration equations are derived by considering small perturbations about the spinning equilibrium configuration. Both flexural rigidity and membrane restoring forces due to spin are considered. Known techniques for the solution of stationary shell problems are extended to the more difficult case of the spinning shell. Plots of transverse frequency as a function of shell geometry are presented for the first two modes for shells with one and two nodal diameters for various values of inertia loading. Continuous transition from shell to flat disk results with increasing shell radius of curvature is shown.

Nonlinear Free Vibration of a Double-Deck Reticulated Shallow Spherical Shell

2011 ◽  
Vol 94-96 ◽  
pp. 350-357
Author(s):  
Yong Li ◽  
Jia Chu Xu
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Shallow Spherical Shell ◽  
Linear Vibration ◽  
Model Function ◽  
Nonlinear Free Vibration ◽  
Linear Effect ◽  
Small Deflection ◽  
Non Linear ◽  
Theory Solution

This paper deals with non-linear free vibration of double-deck reticulated shallow spherical shell by applying the non-linear theory of double-deck reticulated shallow spherical shell established by the author. Model function is supposed to be theory solution of small deflection. The proper equation of double-deck reticulated shallow spherical about time functions with two types of boundary conditions is derived by using Galerkin’s method. At the same time, the analytical expression of ratio of non-linear vibration and linear vibration is deduced and the non-linear effect about amplitude is discussed. Numerical examples are given as well.

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