A new computational method for transient dynamics including the low‐ and the medium‐frequency ranges

This paper deals with a new computational method for transient dynamic analysis which enables one to cover both the low- and medium-frequency ranges. This is a frequency approach in which the low-frequency part is obtained through a classical technique while the medium-frequency part is handled through the Variational Theory of Complex Rays (VTCR) initially introduced for vibrations. Preliminary examples are shown.

[1]  A. Sarkar,et al.  Mid-frequency structural dynamics with parameter uncertainty , 2001 .

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

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

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

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

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

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

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

[9]  E. Brigham,et al.  The fast Fourier transform and its applications , 1988 .

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

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

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

[13]  Pierre Ladevèze,et al.  Reduced bases for model updating in structural dynamics based on constitutive relation error , 2002 .

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

[15]  R. Langley On the vibrational conductivity approach to high frequency dynamics for two-dimensional structural components , 1995 .

[16]  Pierre Ladevèze,et al.  Calculation of medium-frequency vibrations over a wide frequency range , 2005 .

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

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

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

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

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

[22]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .