A recent study by Shang [1] outlines an analytical vibration analysis for a hermetic capsule that is described as a circular cylinder closed with hemispherical caps at both ends. Shang's [1] analysis is based upon Naghdi-Reissner shell theory and includes shear deformation. The frequency of vibration results recorded by Shang [1] compare well with previous results given by Tavakoli and Singh [2] and .
O Ozakca and Hinton [3]. Tavakoli and Singh [2] studied the hermetic capsule using Love's shell equations and recorded symmetric and antisymmetric frequencies for free vibration. Later, .
O Ozakca and Hinton [3] verified the results for the same hermetic capsule using a shell finite element based upon Mindlin-Reissner theory that included shear deformation and rotary inertia effects. . O Ozakca and Hinton [3] not only tabulated the symmetric frequencies but independently verified the vibration analysis. The capsule that was studied in references [1-3] had a radius to wallthickness ratio of approximately 50 and would qualify as a thin shell. It would seem reasonable that theories that include shear deformation would agree with the more classic thin shell equations.
The present study extends the analysis to include a somewhat thicker hermetic capsule. A three-dimensional axisymmetric finite element based upon the equations of elasticity in cylindrical co-ordinates is used to model the capsule. The results discussed in the previous paragraph were used to verify the formulation and subsequent analysis. Additional torsional frequencies were found that were not previously reported.
Non-dimensional frequencies are tabulated for the capsule, while the thickness and length of the cylindrical section of the capsule are varied. Representative mode shapes are shown for symmetric, antisymmetric and torsional frequencies.
2. FINITE ELEMENT MODELS
A nine-node Lagrangian isoparametric finite element was used to model the crosssection of the capsule. The finite element was derived in axisymmetric two-dimensional cylindrical co-ordinates following the discussion given by Buchanan [4] for axisymmetric elasticity in r,y,z co-ordinates. The three-dimensional strain-displacement equations and the formulation that extends the two-dimensional finite element analysis to represent a three-dimensional analysis has been outlined by Buchanan and Chua [5]. The governing three-dimensional elasticity equations are satisfied by assuming a periodic solution that