### Complete characterization and synthesis of the response function of elastodynamic networks

Milton, G *(Utah)*

Wednesday 28 July 2010, 09:00-10.00

Seminar Room 1, Newton Institute

#### Abstract

In order to characterize what exotic properties elastodynamic composite materials with high contrast constituents can have in the continuum it makes sense to first understand what behaviors discrete networks of springs and masses can exhibit. The response function of a network of springs and masses, an elastodynamic network, is the matrix valued function W(omega), depending on the frequency omega, mapping the displacements of some accessible or terminal nodes to the net forces at the terminals. We give necessary and sufficient conditions for a given function W(omega) to be the response function of an elastodynamic network assuming there is no damping. In particular we construct an elastodynamic network that can mimic any achievable response in the frequency or time domain. It builds upon work of Camar-Eddine and Seppecher, who characterized the possible response matrices of static three-dimensional spring networks.
Authors: F. Guevara Vasquez (University of Utah), G.W. Milton (University of Utah), D.Onofrei (University of Utah)

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