Abstract
For the analysis and design of acoustical, mechanical and electromechanical systems, the equivalent electrical circuit analogy is widely utilized, which is in particular by favoured by electromechanical engineers. The equivalent electrical circuit results from a process to represent the general three-dimensional system approximately with a corresponding nondimensional discrete network. A Helmholtz' resonator can equivalently be represented by the parallel circuit of a lumped inductor and a capacitor, and an acoustic tube by the distributed transmission line of parallel wires. The former is available for the resonator whose dimensions are much smaller than the sound wave-length under consideration, and the latter for the tube whose diameter is much smaller than the sound wavelength as well. In general acoustic field systems, however, the wave equation is to be solved under proper boundary conditions. The finite difference method is useful for the numerical analysis. Arai developed the equivalent electrical circuits based on the finite difference method and investigated acoustic filters and sound-absorbing wedges by use of the corresponding electric simulators. Now the finite element method is being high-lighted. In this paper are presented equivalent electrical circuits for acoustic fields based on the finite element method. A fundamental equivalent electrical circuits is developed for a liner triangular or tetrahedral acoustic element (Fig. 4 and 5), from which the equivalent circuit for an arbitrary sound field can be formed simply by connection. As is always the case, the treatment at the boundaries is simpler than that of the finite difference method. When the equivalent circuit is once developed, its analysis is usual by possible not only in the frequency-domain but also in the time-domain as an impulse response.
