Local /global homogenization of periodic structures

A novel homogenization method for periodic structures that utilizes a local/global decomposition of the original problem is presented. In the case of periodic structures the global part of a solution is represented as the smoothest solution recovering important information about the structural response. The global solution can also be described conveniently in terms of Bloch waves on periodic structures.;The global problem is self-contained. Local solutions can be reconstructed after the fact, if desired. Global problems are constructed for infinite structures with periodic impedance discontinuities in vacuo. In the case of finite structures with impedance boundaries new boundary conditions are formulated for global problems. As a result, the global problem does not contain discontinuities, has a smooth response; requires less computational effort and recovers important information about the exact solution; such as displacements of discontinuities. Moreover, the global problem can be set up to recover moments of displacement between discontinuities; which are important for prediction of acoustic characteristics.;Coupled fluid-loaded infinite structures are further analyzed. In order to recover acoustic response the law-wavenumber part of spectrum is retained in the global solution. Radiating acoustic modes are contained in the smooth global problem, and the global structural operator accounts for an influence of evanescent acoustic modes. A fluid loading approximation is introduced as a tool to simplify the homogenization of interaction between fluid and structure. This approximation effectively incorporates hydrodynamic loading from higher non-radiating harmonics as an added inertia to the structure. Model scattering problems are solved to investigate the degree of accuracy under this approximation. Accurate results are obtained from this overall method.;Finite periodic structures under fluid loading are considered. The boundary element method for their solution is studied in detail. The question of applying the homogenization technique to methods of this class is addressed. The methods to describe new homogenized boundary elements are discussed. The smoothing of the problem results in lower required resolution and larger boundary elements, which provide great computational savings.