Wave Based Method for the steady-state vibrations of thick plates

Abstract A commonly used technique for the analysis of the low frequency harmonic response of plates is the Finite Element Method (FEM). Since the computational effort of the FEM increases significantly for higher frequencies, different calculation methods are needed to get accurate results for plate bending problems in the mid and high frequency range. A deterministic method called Wave Based Method (WBM) is able to tackle the mid frequency range due to a higher calculation efficiency. It has already been developed for the Kirchhoff plate theory, which is only accurate for rather thin plates, since shear deformation is neglected. Therefore, in this paper the WBM using a first-order shear deformation theory, the Mindlin plate theory, is developed which makes it applicable to thick plates. Numerical examples with point force excitation are shown.

[1]  R. Lyon,et al.  Theory and Application of Statistical Energy Analysis , 2014 .

[2]  P. Ladevèze,et al.  The variational theory of complex rays for the calculation of medium‐frequency vibrations , 2001 .

[3]  Wim Desmet,et al.  An efficient wave based prediction technique for dynamic plate bending problems with corner stress singularities , 2009 .

[4]  K. Bathe.  Finite Element Procedures , 1995 .

[5]  Chi-Hung Huang,et al.  Stress singularities at angular corners in first-order shear deformation plate theory , 2003 .

[6]  Onur Atak,et al.  "MID-FREQUENCY" CAE Methodologies for Mid-Frequency Analysis in Vibration and Acoustics , 2012 .

[7]  S. Marburg.  SIX BOUNDARY ELEMENTS PER WAVELENGTH: IS THAT ENOUGH? , 2002 .

[8]  M. Aliabadi,et al.  The Boundary Element Method , 2002 .

[9]  Chun H. Wang,et al.  Mindlin plate theory for damage detection: Source solutions , 2004 .

[10]  Wim Desmet,et al.  The wave based method: An overview of 15 years of research , 2014 .

[11]  Gregor Tanner,et al.  Dynamical energy analysis—Determining wave energy distributions in vibro-acoustical structures in the high-frequency regime , 2009 .

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

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

[14]  Wim Desmet,et al.  A Wave Based Method for the efficient solution of the 2D poroelastic Biot equations , 2012 .

[15]  Pierre Ladevèze,et al.  The Variational Theory of Complex Rays: An answer to the resolution of mid-frequency 3D engineering problems , 2013 .

[16]  Wim Desmet,et al.  An efficient wave based prediction technique for plate bending vibrations , 2007 .

[17]  Andrew N. Norris,et al.  FLEXURAL WAVE PROPAGATION AND SCATTERING ON THIN PLATES USING MINDLIN THEORY , 1997 .

[18]  Onur Atak,et al.  The Wave Based Method , 2012 .

[19]  Gregor Tanner,et al.  Dynamical energy analysis on mesh grids: A new tool for describing the vibro-acoustic response of complex mechanical structures , 2014 .

[20]  A Carcaterra,et al.  High frequency vibration analysis by the complex envelope vectorization. , 2007, The Journal of the Acoustical Society of America.

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

[22]  Stefano Giani,et al.  Wave transport in complex vibro-acoustic structures in the high-frequency limit , 2011 .

[23]  Caroline Vanmaele.  Development of a wave based prediction technique for the efficient analysis of low- and mid-frequency structural vibrations , 2007 .

[24]  R. D. Mindlin,et al.  Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates , 1951 .

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

[26]  Singiresu S. Rao.  Vibration of Continuous Systems , 2019 .

[27]  P. Pinsky,et al.  Complex wavenumber Fourier analysis of the p-version finite element method , 1994 .

[28]  Laurent Maxit,et al.  Extension of SEA model to subsystems with non-uniform modal energy distribution , 2003 .

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

[30]  V. Cotoni,et al.  Response variance prediction for uncertain vibro-acoustic systems using a hybrid deterministic-statistical method. , 2007, The Journal of the Acoustical Society of America.