Locally resonant metamaterial for the regulation of damage-related nonlinearity based on second harmonic generation

A nondestructive testing method based on nonlinear vibration is usually implemented by measuring the intensity of the second harmonic signal. However, such intensity is much lower than that of the fundamental frequency signal. Particularly, without the help of sufficiently sensitive damage indication effect, the second harmonic signal from the small crack damage can be difficult to identify. In this study, locally resonant metamaterial is introduced into the nonlinear vibration-based nondestructive testing, in order to regulate the second harmonic intensity for a sensitive crack detection. First, an analytical model consisting of a mass-spring chain system and added interior local resonators is studied where a nonlinear bilinear stiffness spring is introduce to the chain system to simulate the breathing crack damage. Then, the incremental harmonic balance method is applied to the model to calculate its harmonic response. It is found that the damage-generated nonlinearity can be effectively regulated in a specific excitation frequency range, where the second harmonic intensity is enhanced apparently by the added local resonators. Moreover, analysis on the frequency-space distribution characteristics of the nonlinear signal reveals a special localization phenomenon. A new damage index is then defined to locate the small breathing crack. Finally, numerical verification on a locally resonant rod with damage, i.e. on a continuous system, has been conducted as the extension of the discrete model examined previously. This research can be a good foundation for metamaterial-promoted vibration-based nondestructive testing.