Nonlinear dynamics of hinged-hinged initially curved beams with opening angle from 0 to π: Experimental and numerical studies

The experimental and numerical dynamics of hinged–hinged beams with initial curvature varying from a straight configuration through shallow arches to a half-circle are investigated using 17 specimens. Experimentally, laser scanning vibrometry is employed to identify the natural frequencies and linear mode shapes. The study is further extended to kinematically excited large-amplitude frequency responses exhibiting complex nonlinear dynamics, including hardening/softening behavior, transmissibility effects, vibration mitigation, and mode crossing and veering phenomena. The numerical investigation is based on finite element formulations developed to capture the dynamic characteristics of the considered beam family through modal analysis accounting for inertia and dry friction at the hinges. Selected configurations are subsequently analyzed using the proposed linear-sweep and step-sweep procedures implemented in Abaqus_CAE©. The simulations incorporate physically imperfect boundary conditions and cover both linear and nonlinear responses, including nonlinear mode shapes, activated frequencies identified from spectrograms, and time-domain responses along the beam span. The presented results provide benchmark cases for validating existing theoretical formulations, extending them toward fully coupled nonlinear large-amplitude vibration models, and identifying the limits of their applicability.