Homogenized equations of motion for rod bundles in fluid with periodic structure

Abstract

“Homogenized” or averaged equations of motion are deduced for linear dynamic fluid-structure interactions of rod bundles immersed in an acoustical fluid. The equations define an effective density tensor which couples the fluid and rod accelerations. In the pressure wave equation a sound speed tensor arises. The theory assumes that the bundle consists of a periodic lattice of cells with diameters which are very small in comparison to the bundle diameter and that cell averages are smooth functions in space and time. The derivation is based on Hamilton's principle. For the specific case of circular cylindrical rods in a square pattern the tensors are given numerically and the fluid-structure interaction effects are discussed.