Ultrasonic Spectral Analysis for Characterization of Composites
The attenuation of propagating ultrasound through heterogeneous materials such as fiber reinforced epoxy composites containing chopped fibers with random orientation is predominantly due to scattering from the fibers as well as from discontinuities such as pores and is consequently frequency dependent. In this paper, we determine the frequency dependent attenuation from the downshifted spectra of the transmitted broadband wavepacket. Such a technique, first used for medical ultrasound, can be very useful for characterization of acoustically very lossy composites, because spectral shifts for such materials can be particularly significant. Experimental results and analytical models are presented for the non-destructive characterization of such composites by this method.
In this paper we study the multivariate ANOVA decomposition for $1$-periodic functions on the torus. In particular we use the integral projection operator that leads to the classical ANOVA decomposition. Relationships between the Fourier coefficients of the function and its ANOVA terms lead to special frequency index sets and give an understanding of the decomposition working in the frequency domain. Moreover, we consider the truncated ANOVA decomposition and provide error bounds for approximation in $\mathrm{L}_\infty$ and $\mathrm{L}_2$. We present an approximation method based on the truncated decomposition with regard to a superposition dimension $d_s$.