Energy and phase velocity considerations required for attenuation and velocity measurements of anisotropic composites

Viscoelastic fibre-reinforced composite materials have a number of possible advantages for use in underwater acoustic applications. In order to exploit these materials it is important to be able to measure their complex stiffness matrix in order to determine their acoustic response. Ultrasonic transmission measurements on parallel-sided samples, employing broadband pulsed transducers at 2.25 MHz and an immersion method, have been used to determine the viscoelastic properties of a glass-reinforced composite with uniaxially aligned fibres. The composite measured was constructed from Cytecfiberite's CYCOM 919 E-glass. The theory of acoustic propagation in anisotropic materials shows that the direction of energy propagation is, in general, different from that given by Snell's Law. At 15 degrees incidence, Snell's Law implies a refracted angle of 40 +/- 2 degrees, whereas the energy direction is observed to be 70 +/- 2 degrees. Despite this, the experimental data indicates that the position of the receiving transducer has relatively little effect on the apparent phase velocity measured. The phase velocities measured at positions determined from the refracted angle and energy direction are 3647 and 3652 +/- 50 m s(-1), respectively. However, the amplitude of the received signal, and hence estimate of attenuation, is highly sensitive to the receiver position. This indicates that the acoustic Poynting vector must be considered in order to precisely determine the correct position of the receiving transducer for attenuation measurements. The beam displacement for a 17.6 mm sample at 15 degrees incidence is 9.5 and 40 mm by Snell's Law and Poynting's Theorem, respectively. Measured beam displacements have been compared with predictions derived from material stiffness coefficients. These considerations are important in recovering the complex stiffness matrix.