Effect of specimen geometry on ultrasound diffusion in cement-based aggregates
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Following Carslaw  and as discussed by Becker et al , the diffusion of ultrasonic energy in cement-based aggregates follow the heat diffusion equation. However, due to the finite size of the discs used in experiments by Becker, ultrasound energy is contained within the body for a longer period of time, as compared to . Though the energy content of the disc in reality would eventually decay to zero, due to leaks and other mechanisms, a theoretical study of perfectly adiabatic case is useful to compare the residual energy values to material properties. As a particular example, the input energy sees multiple phenomena inside the material during propagation. The residual energy is this a combined effect of the multiple scattering, dissipative and diffusive processes. This objective of this thesis is to study the relationship between the residual spectral density and specimen geometry. The effort further aims to attribute the difference in the residual spectral energy density values in materials of similar geometry to the varying material properties of the heterogeneous materials. Finally, a study of the error propagation in the estimation is presented, along-with an analytical relationship showing the value of spectral energy density for discs of finite radius and height. Ref: 1. H. S. Carslaw, J.C.J., Conduction of Heat in Solids. 2nd ed ed. 1986: Oxford University Press, USA. 520 2. Becker, J., L.J. Jacobs, and J. Qu, Characterization of cement-based materials using diffuse ultrasound. Journal of Engineering Mechanics, 2003. 129(12): p. 1478-1484.