High-Frequency Response of an Elastic Spherical Shell

1969 ◽  
Vol 36 (4) ◽  
pp. 859-864 ◽  
Author(s):  
David Feit ◽  
M. C. Junger
Keyword(s):  
Spherical Shell ◽  
Flat Plate ◽  
Wave Field ◽  
Classical Solution ◽  
High Frequency ◽  
Natural Frequencies ◽  
Near Field ◽  
Flexural Wave ◽  
High Frequency Response ◽  
Field Response

The classical solution of the point-excited spherical shell, in the form of a normal-mode series, converges poorly for large frequencies. By applying the Watson-Sommerfeld transformation to this series, the response is expressed as a sum of only two terms. These terms can be interpreted, respectively, as the near-field response and propagating flexural wave field of an infinite flat plate, the latter term being multiplied by a factor whose maxima coincide with the natural frequencies of the shell.

Nonmodal Solution of Spherical Shells With Cutouts Excited by High-Frequency Axisymmetric Forces

1970 ◽  
Vol 37 (4) ◽  
pp. 977-983 ◽  
Author(s):  
M. C. Junger
Keyword(s):  
Boundary Conditions ◽  
High Frequency ◽  
Near Field ◽  
Closed Form Solution ◽  
Radial Force ◽  
Form Solution ◽  
Mode Shapes ◽  
High Frequency Response ◽  
Circular Cutout ◽  
Line Loads

A closed-form solution is obtained for the high-frequency response of a thin spherical shell embodying a circular cutout and excited axisymmetrically by a concentrated radial force. The solution is constructed by combining the shell response to the radial exciting force with its response to radial, tangential, and moment line loads applied along the cutout boundary, these line loads being selected to match the boundary conditions. Concise expressions for the shell response are obtained by applying the Sommerfeld-Watson transformation to the slowly converging high-frequency modal series which is thereby reduced to only two terms, viz., an exponentially decaying near-field and a standing or propagating-wave field. These two terms are in the nature of the creeping waves commonly used to formulate electromagnetic or acoustic diffracted wave fields in the short-wavelength limit. The method is illustrated for the simple case of a circular cutout with a clamped boundary, but lends itself to more complicated boundary conditions, viz., intersecting shells or wave guides. The natural frequencies and mode shapes are found from a single, characteristic equation involving trigonometric functions.

Inferring propeller inflow and radiation from near-field response. II - Empirical application

AIAA Journal ◽  
2001 ◽  
Vol 39 ◽  
pp. 1037-1046
Author(s):  
R. J. Minniti ◽  
W. K. Blake ◽  
T. J. Mueller
Keyword(s):  
Near Field ◽  
Empirical Application ◽  
Field Response
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