The Dynamic Stability Of Shallow Arches Considering Geometrical Imperfections

This paper is concerned with the dynamic snap-through of the hinged-hinged sinusoidal shallow arch with geometrical imperfection under timewise distributed load. With the basic assumptions and Galerkin integration the nonlinear governing equation is derived, which is used to investigate the equilibrium configurations of shallow arch. The sufficient condition against dynamic snap-though can be determined through the total energy of the system and the Lyapunov function in the phase space. The effect of the geometrical imperfections on the sufficient condition for stability is studied, and the emphasis is placed on the influences of root locus of critical points and sufficient condition for dynamic stability on the second harmonic imperfection.