DYNAMIC STABILITY CRITERIA FOR CLAMPED SHALLOW ARCHES UNDER TIMEWISE STEP LOADS

The nonlinear problem of dynamic instability of snap-through of clamped shallow arches subjected to timewise step loads is investigated. Established are separate sufficient conditions for stability and for instability. For arches with parameters in certain special ranges, these two sufficient conditions coincide and, thus, yield the necessary and sufficient condition for stability. Specific problems investigated are '%'simple'%' clamped arches under '%'simple'%' loads, clamped sinusoidal arches under uniformly distributed loads, clamped parabolic arches under distributed loads and clamped sinusoidal arches under concentrated loads which may be located eccentrically.