Dynamic Stability of Shallow Arches with the Geometrical Imperfections

The dynamic stability of the hinged-hinged sinusoidal shallow arch with geometrical imperfection under time wise distributed load is investigated in this paper. First, the nonlinear governing equation of shallow arch is derived from the dpsilaAlembert principle and Euler-Bernoulli assumption. And the dimensionless type of the equations, which is used to investigate the equilibrium configurations of shallow arch, is obtained by the Fourier series expansion and the Galerkin integration. Then, with the application of both the nonlinear equation and sufficient condition for stability, the stability of shallow arch with geometrical imperfection is studied. The emphasis is placed on the influences of root locus of critical points and sufficient condition for dynamic stability on the second harmonic imperfection, which is similar to the buckling mode-shape of arch structure. To compare the stability property of imperfect shallow arch with that of perfect arch, the sinusoidal shallow arch with no imperfection is studied before the analysis of effect on imperfection.