Nonlinear coupling and instability in the forced dynamics of a non-shallow arch: theory and experiments

Dynamic instability of a non-shallow circular arch, under harmonic time-depending load, is investigated in this paper both in analytical and experimental ways. The analytical model is a 2-d.o.f. reduced model obtained by using a Galerkin projection of a mono-dimensional curved polar continuum. The determination of the regions of instability of the symmetric periodic solution and the discussion of the post-critical behavior are carried out, comparing the results with the experimental evidence on a companion laboratory steel prototype. During post-critical evolution, both periodic and non-periodic solutions are obtained varying the excitation control parameters. The theoretical and experimental models are analyzed around the primary external resonance condition of the first symmetric mode, in the case of a nearly 2:1 internal resonance condition between the first symmetric and anti-symmetric modes. When the motion loses regularity, synthetic complexity indicators are used to describe, in quantitative sense, the nonlinear response.