Response of an Unlimited Shallow Spherical Shell to an Oscillating Axisymmetric Pressure

摘要

Naghdi and Orthwein, as part of their general treatment to a class of problems involving elastic and viscoelastic infinitely extended shallow spherical shells, obtained a solution in integral form for the transverse displacements of an unlimited elastic shallow spherical shell due to a harmonically varying axisymmetric pressure acting on a small area about the shell's apex. They then stated, however, that this solution did not admit a closed representation. It is the purpose of this note to show that a closed solution is available for a range of shell and frequency parameters. From the displacement, the stress resultants and stress couples are easily obtained. The dynamic solution is shown to reduce to the static solution obtained by Reissner. (Author)