An efficient wave based prediction technique for plate bending vibrations

The finite element method is a commonly used prediction method for dynamic simulations of plate bending problems. A major disadvantage of this method is its practical frequency limitation as its application involves prohibitively large computational efforts at higher frequencies. A newly developed wave based prediction technique pushes up the frequency limit through an enhanced computational efficiency. This paper discusses the principles of the wave based method for convex plate problems. The beneficial convergence rate of the wave based method as compared with the finite element method is verified for various validation examples, which include the most commonly encountered boundary conditions.

[1]  Bert Pluymers,et al.  A review of the wave based prediction technique for efficient interior acoustic analysis , 2005 .

[2]  Wim Desmet,et al.  A WAVE BASED PREDICTION TECHNIQUE FOR THE STEADY-STATE DYNAMIC ANALYSIS OF FLAT PLATE ASSEMBLIES , 2004 .

[3]  Pierre Ladevèze,et al.  The variational theory of complex rays: a predictive tool for medium-frequency vibrations , 2003 .

[4]  Brian R. Mace.  Statistical energy analysis, energy distribution models and system modes , 2003 .

[5]  Miguel C. Junger,et al.  Sound, Structures, and Their Interaction , 1972 .

[6]  J. Jirouseka,et al.  The hybrid-Trefftz finite element model and its application to plate bending , 1986 .

[7]  Wim Desmet,et al.  On the use of the wave based method for the steady-state dynamic analysis of three dimensional plate assemblies , 2004 .

[8]  O. C. Zienkiewicz,et al.  The Finite Element Method for Solid and Structural Mechanics , 2013 .

[9]  W. Desmet.  A wave based prediction technique for coupled vibro-acoustic analysis , 1998 .

[10]  R. MacNeal,et al.  Finite Elements: Their Design and Performance , 1993 .

[11]  Wim Desmet,et al.  Application of an efficient wave-based prediction technique for the analysis of vibro-acoustic radiation problems , 2004 .

[12]  Vincent Cotoni,et al.  Response variance prediction in the statistical energy analysis of built-up systems. , 2004, The Journal of the Acoustical Society of America.

[13]  L. Cremer,et al.  Structure-Borne Sound: Structural Vibrations and Sound Radiation at Audio Frequencies , 1973 .

[14]  Laurent Maxit.  Extension et reformulation du modèle SEA par la prise en compte de la répartition des énergies modales , 2000 .

[15]  O. G. McGee,et al.  Exact analytical solutions for free vibrations of thick sectorial plates with simply supported radial edges , 1994 .

[16]  I. Babuska,et al.  Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions , 1999 .

[17]  Wim Desmet,et al.  Hybrid finite element-wave-based method for steady-state interior structural-acoustic problems , 2005 .

[18]  O. C. Zienkiewicz,et al.  The Finite Element Method: Basic Formulation and Linear Problems , 1987 .

[19]  Arthur W. Leissa,et al.  Vibration of Plates , 2021, Solid Acoustic Waves and Vibration.

[20]  E. Kita,et al.  Trefftz method: an overview , 1995 .

[21]  A. Leissa,et al.  Exact Analytical Solutions for the Vibrations of Sectorial Plates With Simply-Supported Radial Edges , 1993 .

[22]  C. Farhat,et al.  The Discontinuous Enrichment Method , 2000 .

[23]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

[24]  L. Thompson.  On optimal stabilized MITC4 plate bending elements for accurate frequency response analysis , 2003 .

[25]  R. Langley,et al.  Vibro-acoustic analysis of complex systems , 2005 .