Research on nonlinear response analysis of micro-cracks under vibro-acoustic modulation

In view of the complex nonlinear interaction mechanism between acoustic waves and damage in vibration sound modulation technology, this paper derives the kinematic equilibrium equation for linear elastic materials with cracks undergoing infinitesimal deformation using structural mechanics theory. The weak form of the equation is derived by applying the principle of virtual work to calculate the virtual work due to nonlinear changes in crack spacing. This paper also explains the physical origin of high harmonic and sideband signals in the system displacement solution. In addition, a three-dimensional contact model of micro-cracks is constructed to describe the nonlinear effect of contact sound on the crack surface caused by relevant displacement fields. To verify the correctness of the model, two indicators, the modulation index and the damage index, are used to evaluate the simulation results. The results indicate that the interface contact under micro-crack opening and closing motions causes additional nonlinear frequencies and that the nonlinear response increases with excitation amplitude while being relatively sensitive to micron-level cracks. Finally, experimental research is conducted, which confirms the theoretical derivation, and the reliability of the model has been verified.