Transfer matrix of multilayered absorbing and anisotropic media. Measurements and simulations of ultrasonic wave propagation through composite materials

This paper presents an adaptation of the well-known Thomson/Haskell method to introduce anisotropic attenuation into the formulation of the transfer matrix. The expression for the transfer matrix of one elementary ply is modified to take into account the heterogeneity of the generated modes at interfaces between absorbing media. This heterogeneity depends on the direction of propagation and on the anisotropic attenuation of the ply. The transfer matrix of the stratified composite is derived classically from the multiplication of the elementary matrices and leads to the transfer function of the plate. The transmission and reflection coefficients of multilayered viscoelastic anisotropic composite materials can be computed, for any direction of propagation and for any stacking sequence, with a program that requires the viscoelastic characteristics of the ply. The method is tested with PEEK matrix/carbon fibers composites. The viscoelastic properties of the ply were previously measured with a unidirectional composite made of the same elementary ply in a frequency domain where bulk heterogeneous modes can be isolated. To extend these properties to a larger domain, the model assumes that the attenuation is proportional to the frequency. Doing so, the transmission of broadband waveforms can be computed. These waveforms are compared to experimental waveforms transmitted by composites with different stacking sequences.