Adriano Todorovic Fabro

Flexural wave propagation in slowly varying random waveguides using a finite element approach

This work investigates structural wave propagation in waveguides with randomly varying properties along the axis of propagation, specifically when the properties vary slowly enough such that there is negligible backscattering. Wave-based methods are typically applied to homogeneous waveguides but the WKB (after Wentzel, Kramers and Brillouin) approximation can be used to find a suitable generalisation of the wave solution in terms of the change of phase and amplitude, but is restricted to analytical solutions. A wave and finite element (WFE) approach is proposed to extend the applicability of the WKB method to cases where no analytical solution is available. The wavenumber is expressed as a function of the position along the waveguide and a Gauss-Legendre quadrature scheme is used to obtain the phase change while the wave amplitude is calculated using conservation of power. The WFE method is used to evaluate the wavenumbers at each integration point. The flexural vibration example is considered with random field proprieties being expressed by a Karhunen-Loeve expansion. Results are compared to a standard FE approach and to the WKB analytical solution. They show good agreement and require only a few WFE evaluations, providing a suitable framework for spatially correlated randomness in waveguides.

Wave propagation and response statistics of short fibre composites from experimental estimation of material properties

Typically there is variability in the material and geometrical properties of fibre-reinforced composites and this variability is often spatially correlated. Numerical models can predict the response of such panels, but the spatially correlated nature of the variability must be represented within the model. However, characterising the variability, and especially the spatial correlation, is problematic. In this study data is first generated by an automated optical process: light transmissibility measurements are taken of a dry chopped strand mat panel. The intensity of the consequent image is post-processed to describe the fibre density as a random field using the Karhunen-Loeve decomposition. The panel is then cut into beams, from which mobility measurements are taken, providing an ensemble of mobility and natural frequency information. The WKB (after Wentzel, Kramers and Brillouin) approximation, is used in order to find a suitable wave solutions for finite waveguides considering the given random field. Subsequent realisations of the random field are then used to predict the statistics of the vibration response of the beams. Numerical and experimental results show a very good agreement. This approach significantly reduces the computational time when compared to standard Finite Element calculations and provides a suitable framework to account for randomness in the properties.