H -ADAPTIVE REFINEMENT STRATEGY FOR ACOUSTIC PROBLEMS WITH A SET OF NATURAL FREQUENCIES

Abstract

The finite element method has been applied to the analysis of acoustic problems with several natural frequencies and mode shapes. First, a recovery-based error estimation is performed following the well-known procedures of structural problems. Then, an h -adaptive refinement strategy is proposed that leads to a finite element mesh with the minimum number of elements and with a specified error for each of the natural frequencies included in the analysis. The procedure provides a useful numerical tool, since the computational requirements are reduced. In addition, results obtained by means of the minimum element size procedure are shown for comparison purposes. The similarity of the meshes given by the two methods is justified on the basis of the equations that lead to the element size of the mesh. The procedure has been applied to some numerical examples to illustrate its validity.