Double-panel active noise reducing casing with noise source enclosed inside – Modelling and simulation study

The main purpose of the article is to provide a theoretical study of a double-panel active casing by developing a mathematical model for such a dynamical system. The aim of the active casing is to reduce device noise generated to the acoustic environment by controlling vibration of wall panels of the device casing. The article concerns mathematical modeling and simulation of an active casing comprising six double–panel walls mounted to a rigid frame. The casing is considered as a complex coupled vibro-acoustic system, where the wall panels are excited by the acoustic fields inside the casing and by actuators bonded to the wall panels and used for active control. The acoustic field inside the casing is, in turn, produced by the noise originating from the device itself, and the secondary sound generated by all vibrating walls panels. In the first part of the paper a theoretical analysis is performed to derive mathematical model for the system under consideration. The Kirchhoff-Love equations are used to describe walls panels dynamics and the acoustic wave equations are applied to describe acoustic fields in appropriate media. The mathematical model represented as a system of coupled partial differential equations, subject to appropriate boundary conditions, is derived. The fluid–structure interactions of vibroacoustic and acoustic-vibration character, are also incorporated into the model. The model describes also imperfect fastening of the walls panels edges to the rigid frame. All assumptions applied to derive the model are chosen to relate the model to the realities of the utility. In the second part of the paper in order to prove the correctness of the derived model and give a better physical insight into the system, simulations are performed by means of a general-purpose simulation software COMSOL Multiphysics®. Responses to noise generated by a primary source of noise located in the interior of the active casing are investigated there. Simulations conditions are chosen in such a way to demonstrate the model behaves properly in the context of all incorporated vibro-acoustic interactions that can be observed in a real system.