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

In this paper we study the effects of elastic foundation on the static and dynamic snap-through of a shallow arch under a point load traveling at a constant speed. The deformation of the arch is expressed in a Fourier series. For static analysis when the moving speed of the point load is almost zero, the first four modes in the expansion are sufficient in predicting the equilibrium positions and the critical loads. Unlike the case without elastic foundation, static snap-through can occur even when the arch is in another stable (P1-) position before the point load moves onto the arch. In the dynamic case when the moving speed of the point load is significant, the numerical simulation of the response does not converge well, especially long after the point load leaves the arch. However, the total energy of the arch converges quite well when only the first eight modes are used in the Fourier series. This observation allows us to establish a sufficient condition against dynamic snap though, although we are unable to predict precisely, with finite number of modes in the series, at what time it will occur when this sufficient condition is not fulfilled.