A Hermite High-Order Finite Element for Aeroacoustic Analysis

In this paper we assess a finite--element technique based upon a three-dimensional Hermite interpolation for the evaluation of natural modes of vibration of the air inside a cavity (interior acoustics) and/or of elastic structures (structural dynamics), for frequency as high as possible, so as to make the technique useful for aeroacoustics applications, such as coupling of vibrating structures and air. The unknowns are the nodal values of the function (velocity potential for acoustics and displacement forstructural dynamics), of its three partial derivatives, of its three mixed second derivatives, and of its third mixed derivative. Applications include the evaluation of the natural frequencies of the air inside simple geometries, as well as shell-like elastic structures, which are treated as three--dimensional objects, with only one element along the normal (comparisons with commercial-code results are included). The generalization to complex geometries is outlined, with simple example provided. Thepotentiality of Guyan reduction is also assessed.