Homogenization of the von Karman plate equations

A problem of interest in designing control laws for flexible truss structures is the development of models which are simple enough so that solutions can be computed, yet retain the important features of the dynamics. The authors discuss a homogenization approach to modeling and identification in flexible truss structures, based on von Karman's plate equation. Treating the structure as a plate with periodic holes, they derive a homogenized von Karman equation, which is a limit equation as the holes increase in frequency and the amount of material decreases. One can then base identification strategies on the homogenized equation, which holds on a simple domain, rather than on the original equation with its highly complex domain.<
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