| title: | Wave dynamics and wave hierarchy in microstructured materials |
|---|---|
| reg no: | ETF5565 |
| project type: | Estonian Science Foundation research grant |
| subject: |
2.3. Mechanics |
| status: | accepted |
| institution: | Institute of Cybernetics at Tallinn Technical University |
| head of project: | Andrus Salupere |
| duration: | 01.01.2003 - 31.12.2006 |
| description: | The project deals with wave propagation in microstructured materials. The main attention is paid to analysing complicated dispersive and nonlinear effects and to explaining of the influence of the external body force to dynamical processes in microstructured media. The most important phenomenon in this content is the possible emerging of solitons. The project focuses on a very important approach - in order to model the wave motion in microstructured materials best, the concept of wave hierarchy must be used. The idea is following - the ratio of two characteristic length (internal and external) determines the behaviour of the wave-field. The longer waves do not "feel" the microstructure, but the short waves are strongly influenced by it. In governing equations those effects are described by two wave operators weighed by the ratio of characteristic length. In general terms we plan to show how a more general theory (of microstructured continua) can be reduced to less general governing equations (of wave hierarchy) but keeping the governing physical effects. The idea of the project is to build up a solid basis for modelling hierarchical wave processes and to solve several practical problems. The project is closely related to graduate studies - PhD and MSc as well as BSc students are included annually. Schedule for 2002: 1) to derive hierarchical mathematical models describing the wave propagation in microstructured materials; 2) to determine the influence of higher order dispersive and nonlinear effects on the propagation of localised initial excitations in microstructured materials; 2) to study the formation of soliton ensembles in granular materials and analyse of solution types in the case of harmonic initial conditions; 2) to explain the specific influence of different higher order nonlinearities (elastic potentials) on the formation of solitons; 5) to improve and test numerical methods; 6) to finish one BSc and one MSc theses; 6) writing up papers and preparing conference talks. |
| project group | ||||
|---|---|---|---|---|
| no | name | institution | position | |
| 1. | Olari Ilison | Tallinn Technical University | PhD student | |
| 2. | Andrus Salupere | Institute of Cybernetics at Tallinn Technical University | senior resercher | |