Power flow analysis of complex coupled systems by progressive approaches

A generalized mobility,/impedance-power flow mathematical model is develope d to analyze the dynamical behaviour of a complex coupled system consisting of any number of substructures with various configurations and multiple in teraction interfaces. The coupled system is subject to multiple excitations and selected boundary conditions. Generalized mobility/impedance matrix fo rmulations for three-dimensional rigid and elastic structures of general co nfiguration are first derived allowing the construction of equivalent mobil ity (EMM) and equivalent impedance (EIM) matrices to describe the dynamical behaviour of a substructure or a subsystem assembled from several inter-co nnected substructures within the overall system. Based on these two propose d matrices, two progressive approaches are developed to predict the force v ectors and velocity response vectors as well as the power flows into and tr ansmission between substructures in the complex coupled system. The develop ed mathematical model avoids the generalized inverse process associated wit h rectangular matrices when dealing with multi-input/multi-output (MIMO) sy stems in which the dimensions of input and output are different. It is also very flexible and conveniently extended if additional substructures are fu rther connected to the original dynamic system without involving much addit ional computational effort. The proposed methods are shown to reduce the co mplexity of the power flow analysis applied to complex dynamic coupled syst ems and they are applicable to a very large class of dynamical systems in e ngineering. To illustrate and demonstrate their usage, the dynamics of a fl exible raft vibration isolation system is investigated; this comprises two machines, flexible raft, and flexible foundation with connecting isolator a ttachments. (C) 2001 Academic Press.