Nonlinear vibrations of beams with different boundary conditions by a higher-order model and experiments

ABSTRACT A higher-order shear deformation model for nonlinear vibrations of beams with various boundary conditions and made of traditional and advanced materials is developed. The novelty lies in accounting for nonlinearities in bending strains and higher-order shear deformation, which significantly improves accuracy, especially for beams with one or both movable boundary conditions, for which an incorrect nonlinear response is obtained when these effects are neglected. The natural boundary conditions for axially movable and elastic ends are exactly satisfied, which is essential for obtaining accurate results for simply supported movable and cantilever beams. The proposed model is validated through comparisons with results available in the literature for various boundary conditions. Nonlinear responses of the same beam under different boundary conditions are plotted together to highlight the large differences in behavior, ranging from very mild softening to very strong hardening. The effects of flexible axial constraints and one-to-one internal resonance between bending and longitudinal modes are also investigated. Laboratory experiments on nonlinear forced vibrations of cantilever and clamped–clamped immovable beams are conducted to further validate the model. Different beams are tested, including thin steel beams and a laminated sandwich composite beam. The experimental results show very good agreement with the computed nonlinear forced vibration responses. Results show that strong hardening behavior is always linked to axially immovable, or close to immovable, boundary conditions.