Localized waves at a line of dynamic inhomogeneities: General considerations and some specific problems
| Autor: | Alexander Movchan, Gennady Mishuris, Leonid I. Slepyan |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics
Floquet theory Mechanical Engineering Mathematical analysis Rotational symmetry 02 engineering and technology 021001 nanoscience & nanotechnology Condensed Matter Physics 01 natural sciences 010305 fluids & plasmas Discrete system Amplitude Sine wave Mechanics of Materials 0103 physical sciences Harmonic Phase velocity 0210 nano-technology Bloch wave |
| Zdroj: | Journal of the Mechanics and Physics of Solids |
| Popis: | We consider a body, homogeneous or periodic, equipped with a structure composed of dynamic inhomogeneities uniformly distributed along a line, and study free and forced sinusoidal waves (Floquet - Bloch waves for the discrete system) in such a system. With no assumption concerning the wave nature, we show that if the structure reduces the phase velocity, the wave localizes exponentially at the structure line, and the latter can expand the transmission range in the region of long waves. Based on a general solution presented in terms of non-specified Green’s functions, we consider the wave localization in some continuous elastic bodies and a regular lattice. We determine the localization-related frequency ranges and the localization degree in dependence on the frequency. While 2D-models are considered throughout the text, the axisymmetric localization phenomenon in the 3D-space is also mentioned. The dynamic field created in such a structured system by an external harmonic force is obtained consisting of three different parts: the localized wave, a diverging wave, and non-spreading oscillations. Expressions for the wave amplitudes and the energy fluxes in the waves are presented. |
| Databáze: | OpenAIRE |
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