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.

[1]  P. Hager,et al.  Adaptive eigenfrequency analysis by superconvergent patch recovery , 1999 .

[2]  J. Z. Zhu,et al.  The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique , 1992 .

[3]  Pierre Ladevèze,et al.  Error Estimate Procedure in the Finite Element Method and Applications , 1983 .

[4]  J. Z. Zhu,et al.  The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity , 1992 .

[5]  Peter Bettess,et al.  Notes on mesh optimal criteria in adaptive finite element computations , 1995 .

[6]  P. Ladevèze,et al.  Accuracy in finite element computation for eigenfrequencies , 1989 .

[7]  Pierre Ladevèze,et al.  An automatic procedure with a control of accuracy for finite element analysis in 2D elasticity , 1995 .

[8]  Luis Baeza,et al.  Error estimation and h-adaptive refinement in the analysis of natural frequencies , 2001 .

[9]  Ahmet Selamet,et al.  Acoustic Attenuation Performance of Circular Expansion Chambers with Single-Inlet and Double-Outlet , 2000 .

[10]  Grant P. Steven,et al.  NATURAL FREQUENCY ERROR ESTIMATION USING A PATCH RECOVERY TECHNIQUE , 1997 .

[11]  Javier Oliver,et al.  CRITERIA TO ACHIEVE NEARLY OPTIMAL MESHES IN THEh-ADAPTIVE FINITE ELEMENT METHOD , 1996 .

[12]  Ivo Babuška,et al.  Accuracy estimates and adaptive refinements in finite element computations , 1986 .

[13]  I. Babuska,et al.  Finite element solution of the Helmholtz equation with high wave number Part I: The h-version of the FEM☆ , 1995 .

[14]  I. Babuska,et al.  Finite Element Solution of the Helmholtz Equation with High Wave Number Part II: The h - p Version of the FEM , 1997 .

[15]  K. L. Hong,et al.  Natural mode analysis of hollow and annular elliptical cylindrical cavities , 1995 .

[16]  P. Tong,et al.  Mode shapes and frequencies by finite element method using consistent and lumped masses , 1971 .

[17]  Ivo Babuška,et al.  A posteriori error estimation for finite element solutions of Helmholtz’ equation. part I: the quality of local indicators and estimators , 1997 .

[18]  Romualdas Bausys,et al.  Adaptive Finite Element Strategy for Acoustic Problems , 1999 .

[19]  J. Allard,et al.  Superconvergent patch recovery technique for the finite element method in acoustics , 1996 .

[20]  Philippe Marin,et al.  Accuracy and optimal meshes in finite element computation for nearly incompressible materials , 1992 .