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.

使用双线性弹簧模型解释了具有非线性边界条件的梁的实验振动响应。考虑了两个梁系统：一个是单杆，第二个是连接在一起的平行杆簇。对于两个系统，在束端的边界条件由间隔格提供，间隔格是核工业中使用的特定支撑。实验是将光束浸入静水中进行的。实验表征了隔栅对梁施加的非线性边界条件。边界条件从在低振动振幅处具有旋转线性刚度变为在较高振动振幅处具有滞后的双线性。发现双线性刚度属于软化类型。具有粘性阻尼的双线性刚度模型用于解释梁的强迫振动响应。通过在频域中最小化一组实验点与相应数值结果之间的加权距离，可以在任何激励水平下确定模型中使用的刚度和阻尼比。系统的等效粘性阻尼随振动幅度而增加。对于在频率和力-位移域中研究的梁系统，数值和实验结果之间都取得了很好的一致性。通过使用具有附加切换点的分段线性刚度函数并引入非线性阻尼来进一步完善模型。