TOWARD LOCAL EFFECTIVE PARAMETER THEORIES USING MULTIRESOLUTION DECOMPOSITION

Using the recently developed theory of multiresolution decomposition, a formulation that governs the response of a linear, dynamical system with nonstationary, microscale heterogeneity is reduced to two coupled formulations: one governing the response smoothed on an arbitrary cho sen reference scale with the response fine details as forcing, and one governing the response detail with the smoothed response as a forcing . By substituting the solution of the latter in the former, a new fram ework specifically tuned to macroscale variations of the response, in which the effects of the nonstationary, microscale heterogeneity are d escribed via a macroscale-effective material operator, is obtained. Lo calization of across-scale couplings and the dependence of the smoothe d response and the effective material operator on the microscale and m acroscale geometries are investigated asymptotically and numerically. The numerical results are the response of a fluid-loaded elastic plate with nonstationary, microscale mass heterogeneity.