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Coupling Lumped and Boundary Element Methods Using Superposition

Both, the Lumped and the Boundary Element Method are powerful tools for simulating electroacoustic systems. Each one can have its preferred domain of application within one system to be modeled. For example the Lumped Element Method is practical for electronics, simple mechanics, and internal acoustics. The Boundary Element Method on the other hand enfolds its strength on acoustic-field calculations, such as diffraction, reflection, and radiation impedance problems. Coupling both methods allows to investigate the total system. This paper describes a method for fully coupling of the rigid body mode of the Lumped to the Boundary Element Method with the help of radiation self- and mutual radiation impedance components using the superposition principle. By this, the coupling approach features the convenient property of a high degree of independence of both domains. For example, one can modify parameters and even, to some extent, change the structure of the lumped-element network without the necessity to resolve the boundary element system. This paper gives the mathematical derivation and a demonstration-example, which compares calculation results versus measurement. In this example electronics and mechanics of the three involved loudspeakers are modeled with the help of the lumped element method. Waveguide, enclosure and radiation is modeled with the boundary element method.

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