Analysis and optimization of energy flows in structures composed of beam elements – Part II: examples and discussion

Abstract

This paper addresses analysis and optimization of in-plane coupled flexural and longitudinal vibrations within the framework of a theory outlined in a companion paper. An optimization problem is posed for a model structure consisting of two elements of a finite length and one semi-infinite element. This model structure has four terminal points. Parameters of design are chosen as stiffness, mass and the location of two of the terminal points. A parametric study of vibrations of the structure is performed and optimal locations of terminal points are detected. Analysis of energy flows between elementary dynamical systems is done and the dynamics of a structure with the optimized design shape is compared with the dynamics associated with the initial design shape. The formulation of the optimization problem is also extended to include amplitudes of "secondary forces" as design variables. Possibilities of active control of energy flows by usage of "secondary" sources of excitation are discussed.