Theoretical and Experimental Evidence of Symmetric Response Instability in the Finite, Planar Dynamics of a Circular Arch

Abstract

The role of experimental tests as a necessary step in the analysis and the design of slender structures undergoing large displacements is assessed in this paper. In particular, the finite, forced dynamics of elastic structures having initial curvature show a series of interesting phenomena due to the presence of both symmetric and non symmetric nonlinearities. In the case of a circular arch excited by an harmonic vertical load applied on the tip and having the dynamics confined to the plane of initial configuration, the simple unimodal symmetric solution, stable for low excitation levels, loses stability around meaningful resonance conditions, and coupled symmetric anti-symmetric solutions appear. The nonlinear modal coupling is furthermore strengthened by possible internal resonance conditions depending on elasto-geometrical structural parameters and/or on the location of possibly applied concentrated masses.