Analysis Of Elastic Wave Propagation In Periodically Multilayered Structures

The periodically multilayered structure, which consists of periodically arranged multilayers of various materials along the thickness direction, is one kind of one-dimensional(1D) phononic crystals. Due to its periodicity of arrangement, the periodically multilayered structure possesses elastic wave bands, namely the elastic waves with frequencies in pass-bands can propagate without attenuation, while elastic waves with frequencies in stop bands attenuate quickly. These characteristics of elastic wave bands in periodically multilayered structure can be used to control elastic waves, i.e., to filter the elastic waves with frequencies in stop-bands and to enable elastic waves with frequencies in pass-bands to propagate freely. Because of the above application potentiality, the elastic wave propagation in periodically multilayered structures has become a hot research topic in scientific domains such as signal transmission, vibration and noise reduction, precise apparatus processing etc. With regard to ideal models of periodically multilayered structures whose sub-layers in the unit cell are infinite along both the thickness as well as plane directions and are perfectly connected, this thesis studies the in-plane P-SV waves in periodically multilayered isotropic media and the 3D coupled-mode elastic waves in periodically multilayered anisotropic as well as piezoelectric media.First, based on the 2D elasticity of isotropic elastic media, the 3D elasticity of anisotropic elastic media and the 3D piezoelectricity of piezoelectric media, the state equations are derived for layers consisting of these media. On the basis of the wave solutions to these state equations and the Floquet–Bloch principle, the method of reverberation–ray matrix(MRRM) is introduced to the analysis of elastic wave propagation in periodically layered isotropic, anisotropic and piezoelectric media. Unified formulations of MRRM for analyzing the elastic wave propagation in these periodic media are derived.Second, according to the obtained MRRM formulations, computer programs are written with FORTRAN language to compute the dispersion curves of elastic waves in the above–mentioned three kinds of periodically multilayered media. Through numerical examples, the correctness of the computer programs and the numerical stability as well as the accuracy of the MRRM in various frequency ranges are validated.Finally, comprehensive dispersion curves of characteristic elastic waves in the three kinds of periodically multilayered structures are calculated numerically using the above computer programs. The general properties of the dispersion curves of the three kinds of periodically multilayered structures are summarized.From these investigations, the following conclusions are drawn:(1) Among all the dispersion curves, only those frequency-related ones indicate wave bands. As the characteristic waves propagate along the thickness direction, pass band first appears in all the frequency-related dispersion curves. The pass-bands and stop-bands of the same mode alternate in the frequency domain, while the dispersion curves of different modes may overlap in some frequency ranges. As the characteristic waves propagate obliquely to the thickness direction, stop band first appears in all the frequency-related dispersion curves. Besides, some frequency ranges may appear with neither dispersion curves of purely real wavenumbers nor dispersion curves of purely imaginary wavenumbers, which actually pertains to the stop-bands with complex wavenumbers. In the high frequency ranges, the wavenumber in the layer plane has a negligible effect on the dispersion curves of the characteristic waves, because the frequency is a dominant factor in this case.(2) In the phase velocity- and wavelength-related dispersion curves, the phase velocities and the wavelengths both demonstrate multi-value and asymptotic behaviors. In the phase velocity-related dispersion curves, nonzero cutoff phase velocities are perceived at zero frequency.(3) When the anisotropy of the layer materials is strong, the wavenumber-related dispersion curves lose their symmetry about the zero wavenumber, while retain their periodicity about the wavenumber. Some dispersion curves may extend out of the bounding frequencies corresponding to qh=2nπ and/or qh=(2n+1)π.