Theoretical and experimental study of the nonlinear resonance vibration of cementitious materials with an application to damage characterization

This paper presents a theoretical and experimental study of the nonlinear flexural vibration of a cement-based material with distributed microcracks caused by an important deterioration mechanism, alkali-silica reaction (ASR). The general equation of motion is derived for the flexural vibration of a slender beam with the nonlinear hysteretic constitutive relationship for consolidated materials, and then an approximate formula for excitation-dependent resonance frequency is obtained. A downward shift of the resonance frequency is related to the nonlinearity parameters defined in the constitutive relationship. Vibration experiments are conducted on standard mortar bar samples undergoing progressive ASR damage. The absolute nonlinearity parameters are determined from these experimental results using the theoretical solution in order to investigate their dependence on the damage state of the material. With the progress of the ASR damage, the absolute value of the hysteresis nonlinearity parameter increases by as much as six times from the intact (undamaged) state in the sample with highly reactive aggregate; this is in contrast to a change of about 16% in the linear resonance frequency. It is demonstrated that the combined theoretical and experimental approach developed in this research can be used to quantitatively characterize ASR damage in mortar samples and other cement-based materials.