Solutions for the axially symmetric motion of an elastic spherical sandwich shell have been obtained from a theory of shells which includes the effects of transverse shear deformation and rotary inertia. Frequency equations and mode shapes are derived for the full vibrations of a closed spherical shell

Wilkinson, J. P. D.

English

NASA Technical Reports Server

August 1967
	
Brief 67-10279 
NASA TECH BR 
NASA Tech Briefs are issued to summarize specific innovations derived from the U.S. space program, 
to encourage their commercial application. Copies are available to the public at 15 cents each 
from the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
Computer Program for Determination of Natural 
Frequencies of Closed Spherical Sandwich Shells 
The problem: 
To obtain the equations of motion of a spherical 
sandwich shell and to derive frequency equations for 
the free vibrations of a closed shell. Many modern 
shell structures incorporate a sandwich construction 
consisting of a core layer covered by relatively thin 
facing sheets having material properties different from 
the core. The dynamics of such shells have received 
little attention compared with those devoted to shells 
of monocoque construction. Although the analysis of 
shells having simple geometries, such as cylinders and 
spheres, has been considered, the frequencies of 
sandwich shells had to be calculated. on the basis of a 
monocoque shell, and the effects of transverse normal 
stress and transverse shear deformation had to be 
neglected. 
The solution: 
Solutions for the axially symmetric motion of an 
elastic spherical sandwich shell have been obtained 
from a theory of shells which includes the effects of 
transverse shear deformation and rotary inertia. Fre-
quency equations and mode shapes are derived for the 
full vibrations of a closed spherical shell. From these 
equations, a computer program was developed which 
gives the natural frequencies of any elastic spherical 
sandwich shell. 
How it's done: 
The axially symmetric motions of shells of revolu-
tion are either of a torsional or of a torsionless charac-
ter. In the former case the motion is exclusively in the
circumferential direction, while in the latter there is no 
motion in that direction. This program presents fre-
quency equations for both the torsionless and the 
torsional modes of free vibration of the closed sand-
wich sphere. 
Assume that the facing layers have the same mater-
ial properties, are of equal thickness, and are much 
thinner than the core. They carry only direct stress 
and have no flexural rigidity about their own middle 
surfaces. Poisson's ratio is assumed to be the same in 
the facings and the core. The effect of transverse 
normal stress in the core layer is taken into account. 
However, it is assumed that E fh2/ECh I is much larger 
than unity so that the core layer contributes negligi-
bly to the moment resultants and membrane stress 
resultants of the composite shell. Thus the equations 
of motion may be obtained from E. Reissner's paper 
on the statics of sandwich shells with the addition of 
the appropriate inertia terms. 
If the effect of transverse normal stress is neglected, 
that is, if it is assumed that the core layer is infinitely 
stiff in the radial direction, then a simple substitution 
concerning the material and geometric constants 
shows that the uncoupled equations of the present 
analysis have the same form as those obtained for a 
spherical monocoque when the effect of transverse 
shear deformation is retained in the analysis. In that 
case, the frequency equations derived previously by 
Wilkinson for the spherical motiocoque are applicable 
when certain substitutions are made. 
Notes: 
I. The program was written for the IBM 7090/94. 
2. Fortran IV is the programming language used. 
-	 (continued overleaf) 
Now
This document was prepared under the sponsorship of the National 
Aeronautics and Space Administration. Neither the United States 
Government nor any person acting on behalf of the United States
Government assumes any liability resulting from the use of the 
information contained in this document, or warrants that such use 
will be free from privately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19670000279 2020-03-11T20:37:42+00:00Z
Additional details are contained in: Natural Fre-
quencies of Closed Spherical Sandwich Shells, by 
J. P. D. Wilkinson, North American Aviation, Inc., 
S1D65-1604, December 1965. Copies of this report 
are available frqm: 
COSMIC 
Computer Center 
University of Georgia 
Athens, Georgia 30601 
Reference: B67-10279
Patent status: 
No patent action is contemplated by NASA. 
Source: J. P. D. Wilkinson 
of North American Aviation, Inc. 
under contract to 
Manned Spacecraft Center 
(MSC-1246) 
Brief 67-10279	 Category 06


Computer program for determination of natural frequencies of closed spherical sandwich shells

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server