Dynamic Snap-Through of a Shallow Arch Under a Moving Point Load

Abstract

In this paper we study the dynamic behavior of a shallow arch under a point load Q traveling at a constant speed. Emphasis is placed on finding whether snap-through buckling will occur. In the quasi-static case when the moving speed is almost zero, there exists a critical load Qcr in the sense that no static snap-through will occur as long as Q is smaller than Qcr. In the dynamic case when the point load travels with a nonzero speed, the critical load Qcrd is, in general, smaller than the static one. When Q is greater than Qcrd, there exists a finite speed zone within which the arch runs the risk of dynamic snap-through either while the point load is still on the arch or after the point load leaves the arch. The boundary of this dangerous speed zone can be determined by a more conservative criterion, which employs the concept of total energy and critical energy barrier, to guarantee the safe passage of the point load. This criterion requires the numerical integration of the equations of motion only up to the instant when the point load reaches the other end of the arch.

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

“…It is noted that equilibrium position of a shallow arch under a point force at the mid-point is a classical problem and has been presented in (Fung and Kaplan, 1952). However, a more general case when the point load is at an arbitrary position of the arch is not available in the literature except in Plaut (1979) and Chen and Lin (2004b). The following methodology is a concise extension of the method adopted by Chen and Lin (2004b) to the case with elastic foundation.…”

“…Chen and Lin (2004b) argued that for a curved beam with slenderness ratio 10, the effect of axial stress wave on the lateral vibration is negligible unless the traveling speed of the point force is in the range of ten times of the flexural wave speed. In this paper we assume that the moving speed of the point force is well below this range.…”

“…This paper described the behavior of a shallow arch under a point load moving through the span quasi-statically. Chen and Lin (2004b) extended PlautÕs work to study the dynamic snap-through buckling of a shallow arch under a point force moving with high speed. They reported that when the point load is greater than a dynamic critical load there exists a finite speed zone within which the arch runs the risk of dynamic snapthrough.…”

In-plane elastic buckling of pin-ended shallow parabolic arches

“…They derived analytical solutions of circular arches, but their solutions are limited to solid rectangular cross sections. Recently, Pi et al [14], Bradford et al [15], Rubin [16], and Chen and Lin [17][18][19] studied the buckling of shallow arches. In particular, Pi et al [14] and Bradford et al [15] provided solutions of both pin-ended and fixed circular shallow arches.…”

Equilibria and stability boundaries of shallow arches under static loading in a thermal environment

“…Half-sine, circular and parabolic shapes have been studied [15,16,17] and a variety of loading conditions have been investigated, such as concentrated loads [18,19,20], distributed and end moments loads [21,22,23], and variations in the thermal fields or support conditions [5,24,25]. This paper introduces a semi-analytical procedure to find the exact solution to a half-sine pinned shallow arch under transversal loading.…”