A generalised mathematical model and analysis for integrated multi-channel vibration structure–control interaction systems

A generalised mathematical model and analysis for integrated multi-channel vibration control–structure interaction systems are developed. The governing equations describing the interactions between a generalised elastic structure and a multi-channel electromagnetic excitation and control system are derived. Based on these equations, the stability and dynamic response of the system are analysed. The introduction of an additional dynamic impedance matrix between structure and control system allows vibration structure–control interaction mechanisms to be investigated. The generalised theory provides a basis to measure exactly the dynamic parameters of the structure negating any influence of the excitation and control system. It also allows the design of a more effective control system taking into account the interactions of the control system with structural motions and vice versa. To illustrate the general formulations developed and their applications, simple one- and two-channel systems are investigated using non-dimensional parameters.