Mode matching to enhance nonlinear response of local defect resonance

Abstract Activation of mechanical resonance in localized inclusions and defects enables to route the input acoustic energy directly to the defect that dramatically increases its vibration amplitude and shifts into nonlinear regime. The higher harmonics generated in such a nonlinear resonator excited at a fundamental mode are, however, not matched to the higher-order resonances that prevents full development of the maximal higher harmonic response of the resonator. In the experiments, the nonlinear resonant response is studied for a simulated defect of a circular flat-bottomed hole in a Plexiglas plate. Conventional second and third higher harmonic responses for excitation at the fundamental resonance frequency are measured and used to evaluate background nonlinearity parameters of the resonator. An increase by orders of magnitude in these parameters is then obtained as the excitation frequencies are changed in order the second and third harmonics match the higher-order resonances. A similar result is also obtained for a subharmonic excitation: the second harmonic in this case always matches the fundamental resonance frequency and thus manifests the maximum efficiency.