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Characterization of soft, deformable materials using conventional contact-based methods can be challenging due to errors associated with the applied pressure. Therefore, techniques which use non-contact methods to characterize these soft structures are highly desirable. The present work explores the development of a non-contact air-coupled resonant ultrasound spectroscopy (AC-RUS) technique for the characterization of soft materials. A sample of polydimethylsiloxane (PDMS) was mounted as a circular membrane clamped along its periphery and was excited first in the low frequency acoustic range (i<100 Hz) to induce the lower-order resonant vibration modes. The sample was then excited at ultrasonic frequencies (>50 kHz) to excite the higher order ultrasonic modes. A preliminary assumption of linear elasticity was used to analytically model the vibration of a circular membrane, followed by validations using numerical FEM simulations. The analytical and numerical models were then modified to include the effect of viscoelasticity using Kelvin-Voigt and Maxwell models. The resonant models were further used to obtain the elastic constants and viscoelastic parameter from the experimental frequency response curve.

The dislocation string model developed by Koehler, Granato and Lücke has been used to study the contribution of dislocations to the generation of higher harmonics and damping in propagating acoustic waves. The bowing, and subsequent breakaway of dislocation loops at sufficiently high stress amplitudes leads to a stress amplitude dependence of the acoustic nonlinearity and damping. The present work focuses on the development of a model which incorporates the effects of this amplitude dependence in resonant vibration of solid structures. The equation of motion for a harmonically forced nonlinear beam was derived following the classical plate theory, and assuming a material model showing quadratic nonlinearity with linear viscoelasticity. The dislocation contribution was used to express the coefficients in the equation of motion as forcing dependent parameters. The frequency response and resonant frequency shift of the nonlinear beam resulting from the developed model show a deviation from classical nonlinear behavior, including softening-hardening nonlinearity. The models developed here show that the dislocation contribution can be nonclassical in nature.