Ultrasonic resonance in thin two-layer dynamic systems

Ultrasonic measurement of polymer cure has been demonstrated to be a method that can provide material property information for coatings or bonding applications. Often the polymer thickness required in real applications is significantly less than typical ultrasonic wavelengths that may be practically available or suitable for direct amplitude measurements of reflection or transmission coefficients. The cure behaviour of thin layers will be different from that of thicker samples as the cross-linking reaction is usually exothermic and strongly influenced by heat flow in the system. By applying a thin layer of polymer in the thickness range 10–100 µm to an aluminium substrate with thickness of approximately 1 mm we are able to monitor the effects of adhesive cure on the resonant modes of this two-layer system. We describe a simple model that does not take into account ultrasonic attenuation and then an improvement to this model that does take into account ultrasonic attenuation in the polymer through viscoelastic behaviour. We then compare the results of both models with our experimental data. Experimental results show good correlation with the models and help to explain the complicated behaviour observed even when using the simpler model without attenuation. Including attenuation in our model does affect the frequency of the resonant modes, but where this effect is significant the attenuation of that mode is so high that the mode is not observed experimentally. The potential to extract the ultrasonic properties of the polymer layer from these measurements is discussed.