On the Equations of Linear Shallow Shell Theory

1969 ◽  
Vol 48 (2) ◽  
pp. 133-145 ◽  
Author(s):  
E. Reissner ◽  
F. Y. M. Wan
Keyword(s):  
Shallow Shell ◽  
Shell Theory

Comparison of Beam and Shell Theories for the Vibrations of Thin Turbomachinery Blades

1983 ◽  
Vol 105 (2) ◽  
pp. 383-392 ◽  
Author(s):  
A. W. Leissa ◽  
M. S. Ewing
Keyword(s):  
Shallow Shell ◽  
Shell Theory ◽  
Free Vibrations ◽  
Two Dimensional ◽  
Analysis Method ◽  
One Dimensional ◽  
Low Aspect Ratio ◽  
Turbomachinery Blades ◽  
Dimensional Analysis Method ◽  
Beam Theories

A great deal of published literature exists which analyzes the free vibrations of turbomachinery blades by means of one-dimensional beam theories. Recently, a more accurate, two-dimensional analysis method has been developed based upon shallow shell theory. The present paper summarizes the two types of theories and makes quantitative comparisons of frequencies obtained by them. Numerical results are presented for cambered and/or twisted blades of uniform thickness. Significant differences between the theories are found to occur, especially for low aspect ratio blades. The causes of these differences are discussed.

An Integral Equation Solution for Limit Loads Applied to Lugs on Cylindrical Shells

1991 ◽  
Vol 113 (2) ◽  
pp. 308-313 ◽  
Author(s):  
G. N. Brooks
Keyword(s):  
Lower Bound ◽  
Load Distribution ◽  
Shallow Shell ◽  
Shell Theory ◽  
Normal Force ◽  
Cylindrical Shells ◽  
Yield Condition ◽  
Convolution Integral ◽  
Concentrated Load ◽  
Lower Bound Limit Analysis

A lower-bound limit analysis of loaded integral lugs on cylindrical shells is presented. Normal force and circumferential and longitudinal moment loadings on the lug are considered. The equilibrium solution, necessary for a lower bound, is obtained as a convolution integral of the concentrated load solutions of linear shallow shell theory. The load distribution is chosen to satisfy the yield condition everywhere, while maximizing the load. A simplified yield condition in terms of the shell stress resultants is used. Failure is assumed to occur in the shell, not the lug. Encouraging comparisons with available experimental results for moment-loaded rectangular lugs on pipes are presented. The use of shallow shell theory enables the problem geometry to be described by one less parameter than complete shell theory.

Vibrations of Twisted Rotating Blades

1984 ◽  
Vol 106 (2) ◽  
pp. 251-257 ◽  
Author(s):  
A. W. Leissa ◽  
J. K. Lee ◽  
A. J. Wang
Keyword(s):  
Shallow Shell ◽  
Shell Theory ◽  
Analytical Procedure ◽  
Ritz Method ◽  
Two Dimensional ◽  
Algebraic Polynomials ◽  
Shape Information ◽  
Rotating Blades ◽  
Turbomachinery Blades ◽  
Twisted Blade

The literature dealing with vibrations of turbomachinery blades is voluminous, but the vast majority of it treats the blades as beams. In a previous paper a two-dimensional analytical procedure was developed and demonstrated on simple models of blades having camber. The procedure utilizes shallow shell theory along with the classical Ritz method for solving the vibration problem. Displacement functions are taken as algebraic polynomials. In the present paper the method is demonstrated on blade models having camber. Comparisons are first made with results in the literature for nonrotating twisted plates and various disagreements between results are pointed out. A method for depicting mode shape information is demonstrated, permitting one to examine all three components of displacement. Finally, the analytical procedure is demonstrated on rotating twisted blade modes, both without and with camber.

On the Initial Response of a Spherical Shell to a Concentrated Force

1962 ◽  
Vol 29 (4) ◽  
pp. 689-695 ◽  
Author(s):  
M. A. Medick
Keyword(s):  
Spherical Shell ◽  
Shallow Shell ◽  
Shell Theory ◽  
Initial Response ◽  
Shallow Spherical Shell ◽  
Restricted Class ◽  
Concentrated Force ◽  
Elastic Shells

This paper is concerned with the initial response of a restricted class of thin elastic shells to localized transient loadings. Attention is restricted to those shells which are essentially spherical and shallow in a neighborhood of the loading. The initial response within this neighborhood can be approximated by the response of a (shallow) spherical shell segment to a concentrated force within the framework of a modified shallow-shell theory.

On Vibrations of Pretwisted Rectangular Plates

1962 ◽  
Vol 29 (1) ◽  
pp. 30-32 ◽  
Author(s):  
R. P. Nordgren
Keyword(s):  
Shallow Shell ◽  
Shell Theory ◽  
Free Vibrations ◽  
Frequency Equation ◽  
Numerical Results ◽  
The Other ◽  
Torsional Vibrations ◽  
Rectangular Plates ◽  
Simply Supported

This paper contains an analysis of the free vibrations of uniformly pretwisted rectangular plates, utilizing the exact equations of classical shallow-shell theory. Specifically, solutions are given (a) for two opposite edges simply supported and the other two free, and (b) for all four edges simply supported. Numerical results obtained for case (b) are compared with previous results for the torsional vibrations of pretwisted beams. A simple frequency equation is obtained for case (b), permitting a detailed study of the effects of both pretwist and longitudinal inertia.

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