We present an application of the higher order asymptotic homogenization method (AHM) to the study of wave dispersion in periodic composite materials. When the wavelength of a travelling signal becomes comparable with the size of heterogeneities, successive reflections and refractions of the waves at the component interfaces lead to the formation of a complicated sequence of the pass and stop frequency bands. Application of the AHM provides a long-wave approximation valid in the low-frequency range. Solution for the high frequencies is obtained on the basis of the Floquet-Bloch approach by expanding spatially varying properties of a composite medium in a Fourier series and representing unknown displacement fields by infinite plane-wave expansions. Steadystate elastic longitudinal waves in a composite rod (one-dimensional problem allowing the exact analytical solution) and transverse anti-plane shear waves in a fibre-reinforced composite with a square lattice of cylindrical inclusions (two-dimensional problem) are considered. The dispersion curves are obtained, the pass and stop frequency bands are identified.
Imperfect bonding between the constitutive components can greatly affect the properties of composite structures. We propose an asymptotic analysis of different types of imperfect interfaces arising in the problem of conduction through a simple cubic array of spherical inclusions. The performed study is based on the two-scale asymptotic homogenization method. The microscopic problem on the unit cell is solved using the underlying principles of the boundary-shape perturbation technique. The influence of the interface properties on the effective conductivity and on the local potential and flux fields is studied.
The performance of the newly proposed 6-31G(##) basis set for calculating the equilibrium structure and vibrational frequencies of transition metal carbonyl complexes has been studied at the HF and DFT levels of theory. The 6-31G(##) basis set has been constructed by augmentation of the 6-31G basis set by diffuse and polarization functions, which are generated from the corresponding 6-31G basis AOs response functions obtained in the frame of propagator approach. The predicted values of bond distances and vibrational frequencies for the title compounds are in good agreement with the experimental data. The relative energies and HOMO-LUMO gaps were also estimated for the series of MCO complexes.
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