Homogenization of a ribbed cylindrical shell over the full frequency range for efficient calculation of structural-acoustic behavior

Abstract

A homogenization method for complex structures, applicable for all frequencies, is described for a cylindrical shell with periodically spaced ribs. This approach has application to naval and aerospace structures. The homogenization method utilizes a local–global decomposition facilitated by adding and subtracting canceling smooth forces. The smooth global problem has an infinite-order structural operator, and periodic discontinuities are replaced by equivalent distributed suspension terms. The global problem can be solved very efficiently since all rapidly varying scales have been removed. The local problem, which provides transfer function information for the global problem, is solved separately and independently, except for amplitude information from the global problem. Once formulated, the self-contained global problem is solved first, and the local solution can be reconstructed afterwards. In the present work, the ribs are modeled as annular plates periodically attached to the cylindrical shell. The coupled shell equations are re-cast using the method of local–global homogenization, and are solved efficiently using a combination of symbolic manipulation and numerical methods. Comparisons withother solution methods are presented, and the extension to fluid loading is discussed. [Work sponsored by ONR.]