# Dp 626 en

# Propagation elastic waves through locally periodic structures

**Author**: Chaika Hanna

This master thesis presents the propagation of the longitudinal elastic waves through the locally periodic structures excited by a harmonic force. As in many periodic systems, elastic wave propagation through the periodic structures results in the frequency band gaps, or large ranges of the incident wave frequency over which no wave is transmitted. The material of the locally periodic structures has non-uniform profile of the mass density and elastic properties. Cells with non-uniform cross-section, different materials and linearly graded material, constituting the solid rod, are considered. The corresponding model equation is derived. The transfer matrix method is applied to study the elastic waves passing through the inhomogeneous domain. The calculation of the transfer matrices goes through the evaluation of the general solution in the interval containing two regular singular points. Based on the transfer matrices the influence of the chosen parameter values on the transmission coefficient spectrum is studied. The transmission coefficient calculation of locally periodic structures for N repeating cells is calculated with the help of the Chebyshev polynomials.

**Hanna Chaika**, mailto:chaikhan@fel.cvut.cz