Further research on mechanism of strain growth caused by superposition of different vibration modes

•The substrains induced by bending and membrane modes are extracted.•Bending waves are caused due to the difference between the motions of the perturbation and the spherical shell.•The strain growth mainly results from the superposition of the breathing mode and the bending mode with close frequency.•The interaction between membrane vibrations and bending waves influences the amplitudes and the periods of the substrain curves.•The strain growth factor along the spherical shell with the perturbation is cyclic.•With the cyclic feature neglected, the strain growth factor has an inverse relationship with the distance from the symmetric axis. Strain growth threatens the safety of explosion containment vessels and the superposition of different vibration modes is an important cause of strain growth. In this study, the response of a 2D axisymmetric spherical shell with a fully constrained perturbation is investigated through numerical simulation. The substrains induced by membrane and bending modes are extracted to reveal the mechanism of strain growth. The main conclusions are as follows. (1)The strain growth mainly results from the superposition of the breathing mode and the bending mode with close frequency. (2) The interaction between membrane vibrations and bending waves influences the amplitudes and the periods of the substrain curves. (3) The strain growth factor along the spherical shell is cyclic. (4) With the cyclic feature neglected, the strain growth factor has an inverse relationship with the distance from the symmetric axis.