Experimental Tests in the Formulation of Reduced Order Analytical Models in the Planar Dynamics of Circular Arches

The role of the experimental analysis in the formulation of reduced order analytical models of planar arches under a vertical, sinusoidally varying, concentrated force on the tip is analyzed in this work. In particular, the use of the right analytical model able to reproduce the dynamics of arches having different sag to span ratio is discussed. After analyzing and discussing the non-linear analytical models available in the literature to study different families of arches, the minimal model able to reproduce the actual dynamics exhibited by experimental prototypes is considered. The experimental analysis conducted on two different models put into evidence the main phenomena of the forced dynamics and gives useful hints on the number and shape of the basis functions to be used in the analytical reduction. The main dynamical phenomenon exhibited by the arches is the loose of stability of the directly excited simple, I-mode, periodic solution and a complex bifurcation scenario towards different regular and non regular coupled motions where anti-symmetric components of the motion arise.