Higher order asymptotic homogenization for dynamical problems

Mathematics and Mechanics of Solids, vol. 27, pp. 1672–1687

Abstract

In general, asymptotic homogenization methods (AHMs) are based on the hypothesis of perfect scale separation. In practice, this is not always the case. The problem arises of improving the solution in such a way that it becomes applicable if the inhomogeneity parameter is not small. Our study focuses on the higher order asymptotic homogenization for dynamical problems. Systems with continuous and piecewise continuous parameters, discrete systems, and also continuous systems with discrete elements are considered. Both low-frequency and high-frequency vibrations are analyzed. For low-frequency vibrations, several approximations of the AHM are constructed. The influence of the boundary conditions and the system parameters is investigated. The accuracy of the resulting approximation is assessed in numerical simulations.

Authors 5

1. Igor I. Andrianov corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

   Rhein Energie AG, Cologne, Germany

2. Igor V. Andrianov Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

   Rhein Energie AG, Cologne, Germany

3. Igor V. Andrianov Aachen

   National Academy for Public Administration under the President of Ukraine · RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

   Rhein Energie AG, Cologne, Germany

   Dnipropetrovs'k Regional Institute for Public Administration at National Academy for Public Administration under the President of Ukraine, Dnipro, Ukraine

4. Galina A. Starushenko

   National Academy for Public Administration under the President of Ukraine

   Affiliation as printed

   Dnipropetrovs’k Regional Institute for Public Administration at National Academy for Public Administration under the President of Ukraine, Dnipro, Ukraine

5. Evgenij I. Borodin

   National Academy for Public Administration under the President of Ukraine

   Affiliation as printed

   Dnipropetrovs’k Regional Institute for Public Administration at National Academy for Public Administration under the President of Ukraine, Dnipro, Ukraine