AXISYMMETRIC VIBRATION OF HEMISPHERICAL SHELLS

Abstract Free vibration analysis of homogeneous and isotropic annular thin plates by using Green’s functions is considered. The formula of the influence function for uniform thin circular and annular plates is presented in closed-form. The limited independent solutions of differential Euler equation were expanded in the Neumann power series based on properties of integral equations. The analytical frequency equations as power series were obtained using the method of successive approximations. The natural axisymmetric frequencies for singularities when the core radius approaches zero are calculated. The results are compared with selected results presented in the literature.

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Dynamic collapse forces of composite reinforced metal hemispherical shells

Composite Structures ◽

10.1016/j.compstruct.2017.08.072 ◽

2017 ◽

Vol 180 ◽

pp. 831-844

Author(s):

D. Guo ◽

F.P. Yang ◽

X. Wang

Keyword(s):

Hemispherical Shells

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Experimental stress analysis of the attachment region of hemispherical shells with attached nozzles. Part 5a. Nonradial nozzle at 22-1/2 degrees 2.625 in. O.D.--2.500 in. I.D., zero penetration

10.2172/4193358 ◽

1975 ◽

Author(s):

R. L. Maxwell ◽

R. W. Holland

Keyword(s):

Stress Analysis ◽

Experimental Stress ◽

Experimental Stress Analysis ◽

Attachment Region ◽

Hemispherical Shells

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Closure to “Discussions of ‘Influence Coefficients for Hemispherical Shells With Small Openings at the Vertex’” (1955, ASME J. Appl. Mech., 22, pp. 443–444)

Journal of Applied Mechanics ◽

10.1115/1.4011124 ◽

1955 ◽

Vol 22 (3) ◽

pp. 444

Author(s):

G. D. Galletly

Keyword(s):

Influence Coefficients ◽

Hemispherical Shells

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Discussion: “Stresses in Symmetrically Loaded Hemispherical Shells Having Tapered Edges” (Hollister, S. C., 1937, ASME J. Appl. Mech., 4, pp. A11–A15)

Journal of Applied Mechanics ◽

10.1115/1.4008792 ◽

1937 ◽

Vol 4 (3) ◽

pp. A140

Author(s):

Ernest A. Brooks

Keyword(s):

Hemispherical Shells

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Some Results on Axisymmetric Vibration of Spherical Shells of Variable Thickness

Journal of Pressure Vessel Technology ◽

10.1115/1.2929901 ◽

1990 ◽

Vol 112 (4) ◽

pp. 432-437 ◽

Cited By ~ 2

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.

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