The Effect of Spatial Distribution on Dynamic Snap-Through

Abstract

The effect of the spatial distribution of impulsive loads on dynamic snap-through of a shallow circular arch is considered in detail. The Budiansky-Roth criterion is used to establish critical magnitudes of the load for many distributions by numerical integration of an approximate set of equations obtained by Galerkin’s method. It is necessary to distinguish between snap-through on the initial oscillation (immediate) and snap-through occurring during a finite time of the response. Critical magnitudes for both cases are compared to a distribution independent lower bound obtained from an analysis of the critical points. For all distributions considered the lower bound is a less conservative estimate of the critical magnitude for finite time snap-through than for immediate snap-through. The effect of small damping on this conclusion, however, remains an open question.

Characterizing Dynamic Transitions Associated With Snap-Through: A Discrete System

“…Shallow arches typically snap-through in a symmetric mode shape [15][16][17][18][19], and thus a SDOF link arch may be used to qualitatively model this behavior. For deeper arches, i.e., arches with a higher rise-to-span ratio, an asymmetric mode of buckling is typically encountered.…”

Suddenly Applied Loads

“…Thus we see that when = 6, the critical impulse that causes dynamic buckling is given by 2(pτ 0 ) cr = 6.7. Some interesting features associated with this type of problem are described in [31,32] in which impulsive and harmonic loading may lead to counterintuitive behavior. For example, some early studies were conducted by Hsu (e.g., [24]) on shallow elastic arches under the action of various time-dependent lateral loads, including sinusoidal, arbitrary, concentrated, etc.…”

Effects of elastic foundation on the snap-through buckling of a shallow arch under a moving point load

“…In the case when the lateral load is applied dynamically instead of in the quasi-static manner, the critical load will be different from the one predicted statically, see Hoff and Bruce (1954), Humphreys (1966), Lock (1966), Hsu (1967Hsu ( , 1968, Hsu et al (1968), Huang and Nachbar (1968), Fulton and Barton (1971), Sundararajan and Kumani (1972), Lo and Masur (1976), Johnson and Mclvor (1978), Johnson (1980), Gregory and Plaut (1982), Donaldson and Plaut (1983), Patricio et al (1998), Xu et al (2002), Lin and Chen (2003), Chen and Lin (2004a), and Chen and Liao (2005). A comprehensive review on the dynamic instability of shallow arches can be found in the book by Simitses (1990).…”