The effects of various parameters on the dynamic stability of shallow arches against snap-through when subjected to impulsive loads are investigated in this paper. The parameters are the amplitudes of the higher harmonics in the arch shape, the initial thrust, and the stiffness of the elastic supports at the arch ends. The results are expressed in terms of sufficiency regions of stability in a phase space of infinite dimensions, which, in turn, lead to simple and practical energy criteria. The study of the effects of the higher harmonics in the arch shape shows that the sufficiency stability criterion is sensitive only to the second harmonic. Moreover, for a sinusoidal arch with small amounts of imperfection, it is possible to give an explicit formula for the sufficiency criterion. The analysis presented here takes into account all modes in the response; consequently, the results are free from any uncertainties usually associated with most of the approximate analyses.

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