Frequency window method for forced vibration of structures with connected substructures

A novel method is presented to analyze the harmonic forced vibration of a main structure with multiple connected substructures. The response of the combined system is represented in terms of the uncoupled modes of the system components. Then, the response equations are given in terms of rational polynomial expansions for the main structure mobility, substructure impedances, and the forcing function. Next, the uncoupled modes with natural frequencies closest to the excitation frequency are isolated by a frequency window. The essential idea of the frequency window method is to retain full mathematical detail for these modes and to retain only the essential effects from all remaining modes. This results in both a reduction of complexity and computation effort. The method differs fundamentally from mode truncation and Taylor's series methods. Furthermore, the method gives parameters which provide insight into the coupling effects between the main structure and the substructures.