The variational theory of complex rays for the calculation of medium-frequency vibrations

Pierre Ladevèze (1) , Lionel Arnaud (1) , Philippe Rouch (1) , Claude Blanzé (1)

1 LMT - Laboratoire de Mécanique et Technologie

A new approach called the ''variational theory of complex rays'' (VTCR) is developed for calculating the vibrations of weakly damped elastic structures in the medium-frequency range. Here, the emphasis is put on the most fundamental aspects. The effective quantities (elastic energy, vibration intensity, etc.) are evaluated after solving a small system of equations which does not derive from a finite element discretization of the structure. Numerical examples related to plates show the appeal and the possibilities of the VTCR.

Mots clés: Vibration; Variable frequency; Plate structures; Finite-element methods; Statistical energy analysis; Helmoltz-equation; Elastic-waves; 3 dimensions; Scattering; Systems; Dispersion; Acoustics; Radiation

Domaines: Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Pierre Ladevèze, Lionel Arnaud, Philippe Rouch, Claude Blanzé. The variational theory of complex rays for the calculation of medium-frequency vibrations. Engineering Computations, 2001, vol. 18, pp. 193-214. ⟨10.1108/02644400110365879⟩. ⟨hal-00854453⟩