Analytic, numerical and experimental techniques to formulate four‐pole matrices for hybrid system modeling

Abstract

Four‐pole matrix is a very convenient concept in modeling composite acoustic systems; however, its application has been largely limited to the systems composed of one‐dimensional and lumped parameter components as four poles are defined in terms of the acoustic quantities at points. In this work, four‐pole parameters of a three‐dimensional rectangular cavity are formulated by analytical, numerical and experimental methods according to a general procedure that utilizes the pressure response functions. Results from three methods are compared and confirmed to be very close to one another, which validates the procedure. Therefore, the technique allows formulating the equation of a complex acoustics system by assembling sub‐system equations obtained by applying any method, experimental, analytical or numerical, most suitable to modeling the sub system. Some practical issues that arise in the modeling process such as source modeling, convergence problems and measurement techniques are explained. The procedure developed in this work enables modeling of practically any acoustic system, regardless of its size, shape, and complexity, as long as the system has definable input and output ports.