B. Z. Steinberg
Dept. of Interdisciplinary Studies, Faculty of Eng., Tel Aviv Univ., Tel Aviv, 69978 Israel
J. J. McCoy
Catholic Univ. of America, Washington, DC 20064
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 smoothed response, on an arbitrary chosen reference scale with the response fine details as forcing, and one governing the detail response with the smoothed response as a forcing. By substituting the formal solution of the latter in the former, a new framework, specifically tuned to macroscale variations of the response, in which the effects of the nonstationary microscale heterogeneity are described via a macroscale-effective material operator, is obtained. Localization of across-scale couplings, as well as the dependence of the smoothed response and the effective material operator on the microscale and macroscale geometries are investigated via general asymptotic considerations and specific numerical examples. The latter concerns the response of a fluid-loaded elastic plate with nonstationary microscale mass heterogeneity.