Operational response prediction for rigidly linked structures via direct inversion method

Abstract

Most of the mechanical systems are composed of different subsystems connected and coupled by several links. Any excitation acting on the system is divided into several internal forces which propagate through these links or so-called transfer paths. For these kinds of systems, it is important to predict the structure’s response due to this excitation which is transmitted via propagation paths. Predicting the operational response as much as accurate at the point of interest is of great importance in terms of design optimization and condition monitoring at where the response cannot be measured due to some physical constraints. In accordance with this purpose, the identification of operational internal forces is necessary. In cases where direct measurement of the operational forces is impossible or impractical, especially for complex structures, a common approach is to identify the operational forces based on measured frequency response functions and a set of measured operational responses. The classical approach is the Moore–Penrose pseudo inversion, which needs significant number of frequency response function measurements and huge time consumption and effort since the coupled system is to be disassembled at all interfaces. Noting that, real complex structures have some physical limitations to be disassembled, more practical and faster approaches are required for real-life applications. The aim of this study is to present direct inversion method to identify the operational forces and hence, predict the operational response for rigidly linked vibrating structures and also demonstrate the effect of mass loadings of the transducers and noise during frequency response function measurements. The algorithms investigated herein are applied in numerical and experimental setups composed of rigidly linked structures.