Liu Bie Ju Centre for Mathematical Sciences
City University of Hong Kong
Mathematical Analysis and its Applications
Colloquium

Organized by Prof. Philippe G. Ciarlet and Prof. Roderick Wong

An Asymptotic Procedure for High-Frequency
Homogenization of Periodic Media

by
Professor Julius Kaplunov
Department of Mathematical Sciences
Brunel University
Uxbridge,UK

Date: Feb 24, 2010 (Wednesday)
Time:4:30 pm to 5:30 pm
Venue: Room B6605 (College Conference Room)
Blue Zone, Level 6, Academic Building
City University of Hong Kong

ABSTRACT: An asymptotic procedure based upon a two-scale approach is developed for high-frequency vibration of periodic media. The medium is assumed to have a microstructure with a characteristic length-scale far less than that of the typical wavelength. We exploit the similarity with the so-called high-frequency long-wavelength limit, which have been earlier developed in the linear theory for thin elastic shells. By perturbing about the high-frequency resonances of the elementary cell, long-wavelength equations are deduced, only explicitly dependent on the macro-scale. These equations are applied to Floquet-Bloch waves to identify Block spectra near the edges of the Brillouin zone. The proposed methodology is also extended to discrete lattices. As an example, the hierarchy of homogenized models is derived for the simplest 2D two-mass lattice.

This is joint work with R.V.Craster (University of Alberta) and A.Pichugin (Brunel, University).

** All interested are welcome **

For enquiry: 3442-9816