Ultrasonic interference and critical attenuation in metal-plastic bilayer laminates

Abstract

The resonance of ultrasonic waves in a metal-plastic bilayer laminate placed in an infinite medium is theoretically investigated, and critical attenuation is shown to occur under specific conditions. The bilayer laminate is subjected to normal wave incidence from the side of the plastic layer. Based on a linear viscoelastic model, the amplitude of the reflection spectrum for the laminate is formulated to obtain the exact results for wave resonance and critical attenuation by numerical calculations. Furthermore, the approximate formulae for the conditions of the resonance and critical attenuation are derived explicitly by Taylor expansions with respect to the loss factor of the plastic. As a result, the exact solution shows that the resonance frequencies of the plastic layer slightly increase with increasing loss factor. Their variation with the loss factor agrees well with the second-order approximation result but is insignificant in the cases of common plastics with relatively low loss factors. The exact results also show that the amplitude at each order resonance depends on the loss factor and has a minimum at a critical loss factor. The obtained critical loss factor decreases with increasing resonance order and is well reproduced by the zeroth-order approximation. Experiments are performed on two types of metal-plastic bonded laminates, demonstrating that the measured reflection spectra are in good agreement with the theoretical predictions. In particular, the amplitude of the measured reflection spectrum decreases significantly at a resonance frequency, which is theoretically predicted to satisfy the critical attenuation condition.