Analysis and optimization of energy flows in structures composed of beam elements – Part I: problem formulation and solution technique

Abstract

The paper addresses the analysis of in-plane coupled flexural and longitudinal vibrations of a structure composed of elastic tubular beams. Emphasis is put on optimization of structural performance in terms of minimization of total power flow over a broad-banded frequency range, i.e. minimization of the emitted/trans- mitted energy of vibrations. The objective function is chosen as an energy outflow (a structural intensity) integrated within the given frequency range at a given remote point (cross-section) of the tubular structure. To gain insight into the physical mechanisms of energy transportation, the structure is decomposed into a set of elementary dynamical systems. These elementary dynamical systems (subsystems) are chosen as one-dimensional wave-guides carrying either longitudinal or flexural waves. Vibrations of each dynamical subsystem are described by a boundary equation method, a novel method in structural dynamics which ideally fits the substructuring concept since it deals with physical variables at boundaries between substructures, no matter what type of excitation is applied at individual substructures. A system of boundary integral equations is accomplished by continuity conditions at interfaces between subsystems and by boundary conditions. Since Green's functions used in the boundary integral formulation satisfy the radiation principle, the governing system of equations is equally applicable for analysis of vibrations of both finite-length structures and the structures having infinitely long elements jointed with elements of finite length.