Basic characteristics and accuracy of acoustic element using spline function in finite element sound field analysis

A 27-node isoparametric acoustic element, namely Sp1 27, using the spline interpolation polynomials for the analysis of sound fields in rooms is presented first. Next, the basic characteristics of the element are discussed by comparing with the conventional elements in the eigenanalysis of a small room. Then, the mechanism of causing errors in eigenanalysis is investigated to propose error-characteristic curves as proper guidelines for the appropriate applications of the elements. An example application on a three dimensional sound field proved that, if the size of elements satisfies the value given by the guideline, Sp1 27 can be expected to provide both fair eigenfrequency approximation within 1% relative error and exact modal order agreement with the analytic solution. Finally, its application to a one-dimensional sound field proved that the guideline estimated by the error-characteristic curves give satisfactory results in the approximation of sound pressure waveforms. The basic relation between the eigenmode approximation and resulting sound pressure response was clarified through the process.