Modelling of coupled vibro-acoustic interactions in an active casing for the purpose of control

Abstract The aim of active casing is to reduce device noise generated to the acoustic environment by controlling vibrations of the walls of the device casing. The article concerns theoretical modelling of an active casing composed of six walls mounted to a rigid frame. The casing is considered as a complex coupled vibro-acoustic system, where the walls are excited by the acoustic field inside the casing, and by actuators bonded to the walls and used for active control. The acoustic field inside the casing is, in turn, formed by the noise originating from the device itself, and the secondary sound generated by all vibrating walls. The structure of such system is described in detail and, after being represented as interconnected subsystems, its state-space model is developed. The model includes fluid loading effect and imperfect fastening of wall edges to the frame. The system of coupled partial differential equations, subject to defined boundary conditions, is reformulated as an abstract first order evolution equation in an appropriate infinite dimensional function space. All assumptions and the structure of the model are chosen to make it useful for the purpose of control. In particular, the model can be used for analysis of controllability and observability of the whole casing as a vibro-acoustic system and, based on that, for optimisation of placement of actuators and structural sensors to efficiently reduce noise over required frequency band. On the basis of the obtained state equation, a block diagram of the system is constructed. It shows the structure of the whole system and the nature of interactions occurring between distinguished subsystems.