Enclosure Acoustics Modeling and Control Utilizing a FEM-BEM Approach

Abstract

The subject of this paper deals with developing analytical relations, computational models and active noise controller designs to help tailor of the transmission, dissipation, and the impedance of acoustic energy across an actively controlled boundary. First presented is a brief background of the theory of acoustic noise in reverberant enclosures. The boundary element formulation of the Helmholtz Integral Equation is presented, along with a finite element method (FEM) structural model. Then, an approach for coupling the models and producing a fully coupled linear control design model is presented. These developments are then specifically applied to a 3-D acoustic chamber consisting of two separate 4ft × 4ft × 8ft open ended enclosures separated by a removable actively controlled partition. The way acoustic energy interacts with an active structural boundary is then explored in greater detail using these control design models. A reduced order coupled model is then produced to investigate tailoring a controller for the desired dissipation, impedance, or transmission across boundary. LQG based controllers were investigated in this paper and an evaluation of passivity based controllers is currently underway. The resulting models and design have provided insight that will allow the design of novel structures and controllers that can be tailored for a desired acoustical transport behavior. These models and designs will be validated on an experimental test bed with the same characteristics as the chamber simulated. Future efforts will extend the FEM-BEM modeling strategy to optimize both the structural design, and the active control system to complement each other more effectively.

Enclosure Acoustics Modeling and Control Utilizing a Passive and Active Structural Tailoring

“…Now considering the example system of this paper (two identical enclosures separated by the plate) Equations (5) and (6) can now be formulated into a 2 * n dimensional state space representation (with n equal to the combined number of structural and acoustic modes). More details about the construction of this state space system may be found in [7].…”

“…The finite element model of the plate was created using FEMLAB and was validated for accuracy using ANSYS. In [7] more details of a simple boundary element code that was used to find the natural eigenfrequencies and eigenmodes of the acoustic enclosures are presented. In general, this would be a preferable way of finding the acoustic model as any number of geometries and impedance conditions on the boundary could be accounted for.…”