Spectral analysis of a PM space in the simulation of nonlinear ultrasonic wave propagation

Various models have been proposed for the simulation of classical and nonclassical effects on the propagation of ultrasonic waves in nonlinear mesoscopic elastic materials. They usually assume the presence of a large number of soft interstices, which are responible for the nonlinear and hysteretic behavior of the material. In order to simpify the treatment, a so-called "PM space" of pairs of preassigned interstice strain states and corresponding pressure values, at which transitions from one state to the other are assume to take place, is often considered. The relationship between the choice of the PM spce and teh consequent nonlinearity is, however, inferred only phenomenologically. Starting with the case of only one interface, the interdependence among the parameters of the model, the input excitation, and the spectral contents of the specimen`s response is derived analytically. The results are related to the strains and restoring forces as present in thin bonded interfaces.