Frequencies of vibrations of a spherical shell with all-around pressure

In a previous paper, Shrivastava (2002), had derived the pressures for non-axisymmetric bifurcation buckling of sandwich shells when its faces are stressed in the strain hardening range of plasticity. Here, frequencies and mode shapes of free vibrations of thin elastic spherical shells are derived in the presence of an all-around external or internal (gas) pressure. Similar to the bifurcations under external pressure, it is shown that there are multiple non-axisymmetric modes for single frequencies.