Calculation of medium-frequency vibrations over a wide frequency range

Abstract An enhancement of the “variational theory of complex rays” (VTCR) is being developed in order to calculate the vibrations of slightly damped elastic structures in the medium-frequency range. Here, the emphasis is put on the extension of this theory to the analysis over a wide frequency range. The solution is sought in the form of an original decomposition: the mean value and its complementary part over the frequency range. Numerical examples show the capability of the VTCR to predict the vibrational response of a structure in a frequency range.

[1]  Mohamed Ichchou,et al.  ENERGY FLOW ANALYSIS OF BARS AND BEAMS: THEORETICAL FORMULATIONS , 1996 .

[2]  P. Bouillard,et al.  A wave-oriented meshless formulation for acoustical and vibro-acoustical applications , 2004 .

[3]  Paul E. Barbone,et al.  Scattering by a hybrid asymptotic/finite element method , 1998 .

[4]  Pierre Ladevèze,et al.  Extension of the variational theory of complex rays to shells for medium-frequency vibrations , 2004 .

[5]  I. Babuska,et al.  The generalized finite element method , 2001 .

[6]  M. Malhotra.  EFFICIENT COMPUTATION OF MULTI-FREQUENCY FAR-FIELD SOLUTIONS OF THE HELMHOLTZ EQUATION USING PADÉ APPROXIMATION , 2000 .

[7]  O. Cessenat,et al.  Application of an Ultra Weak Variational Formulation of Elliptic PDEs to the Two-Dimensional Helmholtz Problem , 1998 .

[8]  Mohamed Ichchou,et al.  ENERGY MODELS OF ONE-DIMENSIONAL, MULTI-PROPAGATIVE SYSTEMS , 1997 .

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

[10]  P. Bettess,et al.  Plane wave interpolation in direct collocation boundary element method for radiation and wave scattering: numerical aspects and applications , 2003 .

[11]  Christian Soize,et al.  Linear dynamic analysis of mechanical systems in the medium frequency range , 1986 .

[12]  I. Babuska,et al.  Dispersion analysis and error estimation of Galerkin finite element methods for the Helmholtz equation , 1995 .

[13]  Charbel Farhat,et al.  A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime , 2003 .

[14]  T. Hughes.  Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods , 1995 .

[15]  Christian Soize,et al.  Reduced models in the medium frequency range for general dissipative structural-dynamics systems , 1998, European Journal of Mechanics - A/Solids.

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

[17]  Peter Monk,et al.  A least-squares method for the Helmholtz equation , 1999 .

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

[19]  Edmund Chadwick,et al.  Modelling of progressive short waves using wave envelopes , 1997 .

[20]  Wim Desmet,et al.  A computationally efficient prediction technique for the steady-state dynamic analysis of coupled vibro-acoustic systems , 2000 .

[21]  R. Lyon,et al.  Power Flow between Linearly Coupled Oscillators , 1962 .

[22]  Isaac Harari,et al.  Improved finite element methods for elastic waves , 1998 .

[23]  Yan Zhang,et al.  Multiple scale finite element methods , 1991 .

[24]  Christian Soize.  Medium frequency linear vibrations of anisotropic elastic structures , 1982 .

[25]  Pierre Ladevèze,et al.  A multiscale computational method for medium-frequency vibrations of assemblies of heterogeneous plates , 2003 .

[26]  Robin S. Langley,et al.  A wave intensity technique for the analysis of high frequency vibrations , 1992 .

[27]  Charbel Farhat,et al.  Residual-Free Bubbles for the Helmholtz Equation , 1996 .

[28]  C. Farhat,et al.  A fast method for solving acoustic scattering problems in frequency bands , 2001 .

[29]  Analysis of Medium-Frequency Vibrations in a Frequency Range , 2003 .

[30]  L. Arnaud,et al.  A new computational method for structural vibrations in the medium-frequency range , 2000 .

[31]  P. Barbone,et al.  Numerical and spectral investigations of Trefftz infinite elements , 1999 .

[32]  R. D. Ciskowski,et al.  Boundary element methods in acoustics , 1991 .

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

[34]  Thomas J. R. Hughes,et al.  Galerkin/least-squares finite element methods for the reduced wave equation with non-reflecting boundary conditions in unbounded domains , 1992 .

[35]  James F. Doyle,et al.  Wave Propagation in Structures , 1989 .