Non-linear dynamics of curved beams. Part 2, numerical analysis and experiments

The aim of this work is to formulate a model for the study of the dynamics of curved beams undergoing large oscillations. In Part 1, the interest was oriented to the formulation of a consistent analytical model and to obtain the equations of motion in weak form. In Part 2, a case-study is considered and the response for various initial curved configurations, obtained by varying the initial curvature, is analyzed. Both the free and the forced problems are considered: the linear free dynamics are studied to detect how the initial configuration affects the modal properties and to enlighten the typical phenomena of frequency coalescence and avoidance; the forced dynamics are then studied for different internal resonance conditions to enlighten the phenomenon of the dynamic instability under a shear periodic tip follower force and to describe the various classes of post-critical motion. The results of experimental tests conducted on a slightly imperfect straight beam prototype are eventually discussed.