Harmonic and subharmonic acoustic wave generation in finite structures

The generation of harmonic and subharmonic vibrations is considered in a finite monodimensional structure, as it is produced by the nonlinear acoustic characteristics of the medium. The equation of motion is considered, where a general function of the displacement and its derivatives acts as the forcing term for (sub)harmonic generation and a series of ‘selection rules’ is found, depending on the sample constrains. The localization of the nonlinear term is also considered that mimics the presence of defects or cracks in the structure, together with the spatial distribution of subharmonic modes. Experimental evidence is given relative to the power law dependence of the harmonic modes vs. the fundamental mode displacement amplitude, and subharmonic mode distribution with hysteretic effects is also reported in a cylindrical sample of piezoelectric material.