Further study on counter-intuitive response of single-degree-of-freedom structures

An energy method was proposed in Li et al. (2008), Int J Impact Eng 35(8):784–94 to determine the counter-intuitive region of the breathing mode response of plane-stress rings, which has different mechanism from the counter-intuitive phenomena observed in beams and plates. This paper extended the energy method for plane-stress rings to plane-strain rings and spherical shells for the determination of the counter-intuitive regions of the breathing mode response. Numerical simulations are conducted to support the predictions based on the energy method.