Nonlinear vibrations of beams with bilinear hysteresis at supports: interpretation of experimental results

Abstract

Experimental vibration responses of beams with nonlinear boundary conditions were interpreted using a bilinear spring model. Two systems of beams were considered: one is a single rod and the second one is a cluster of parallel rods linked together. The boundary conditions at the beam ends, for both systems, were provided by spacer grids, which are specific supports used in nuclear industry. The experiments were conducted with the beams immersed in still water. The nonlinear boundary conditions imposed to the beams by the spacer grids were experimentally characterized. The boundary conditions changed from having a rotational linear stiffness at low vibration amplitudes to bilinear with hysteresis at higher vibration amplitudes. The bilinear stiffness was found to be of the softening type. A bilinear stiffness model with viscous damping was used to interpret the forced vibration response of the beams. The stiffness and damping ratio used in the model were identified at any excitation level by minimizing, in the frequency domain, the weighted distance between the set of experimental points and the corresponding numerical results. The equivalent viscous damping of the system grew with the vibration amplitude. Very good agreement between numerical and experimental results was obtained for both the beam systems studied in the frequency and force-displacement domains. The model was further refined by using a piecewise linear stiffness function with additional switching points and introducing nonlinear damping. The identified model was capable of reproducing the experimental results with accuracy and without the requirement to adjust the parameters at different excitation levels.