Nonlinearity evaluation and damage evolution law of simply supported RC beams based on the FRF similarity measure

Reinforced concrete (RC) beam structures are subject to a certain degree of nonlinearity owing to their material properties and other factors. However, the present evaluation methods for their degree of nonlinearity are only applicable to specific types of excitation. In this study, a nonlinear degree evaluation method suitable for impulse excitation is proposed. The nonlinearity degree (ND) index was defined based on the frequency response function similarity measure, which was used to acquire the structural state and compare multiple states. The effectiveness and noise robustness of the proposed method were verified using numerical examples. Additionally, this method was applied to study the nonlinear damage relationship characteristics of RC beam structures. The normalized value given by the ND index accurately determines the relative nonlinear degree and evolution law of the damage state of simply supported RC beams and further clarifies the nonlinear damage relationship. Finally, the control mechanism of the nonlinear factors was revealed by comparing the nonlinear damage relationships of RC beams with different structural properties. This study provides a simple and effective new method for assessing the degree of nonlinearity in engineering structures and further improves the empirical theoretical system of nonlinear damage relationships for RC beam structures.