A study of the effective properties of mass and stiffness microstructures - A multiresolution approach

The theory of multiresolution decomposition and wavelets is used to study t he effective properties of a thin elastic plate with surface mass density o r stiffness heterogeneity, subjected to time-harmonic forcing. The heteroge neity possesses micro- and macro-scale variations, and has a macroscale out er dimension. It is shown that the microscale mass variation has practicall y no effect on the macroscale plate response, whereas microscale stiffness variation can have a significant effect. We derive an effective constitutiv e relation pertaining to a microscale stiffness variation. It is shown that it is possible to synthesize classes of different stiffness microstructure s that have the same footprint on the macroscale component of the plate res ponse. An effective; smooth, stiffness heterogeneity associated with the cl asses is developed. The results are first derived analytically and then sup ported by numerical simulations.