A Study of the E ective Properties of Mass and Sti ness Microstructures - A Multiresolution Approach

The theory of multiresolution decomposition and wavelets is used to study the e ective properties of a thin elastic plate with surface mass density or sti ness heterogeneity, subjected to time-harmonic forcing. The heterogeneity possesses microand macro-scale variations, and has a macroscale outer dimension. It is shown that the microscale mass variation has practically no e ect on the macroscale plate response, whereas microscale sti ness variation can have a signi cant e ect. We derive an e ective constitutive relation pertaining to a microscale sti ness variation. It is shown that it is possible to synthesize classes of di erent sti ness microstructures that have the same footprint on the macroscale component of the plate response. An e ective, smooth, sti ness heterogeneity associated with the classes is developed. The results are rst derived analytically and then supported by numerical simulations.