ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

3aSA1. The equation of diffusion applied to energy density of vibrating beams.

Myriam Djimadoum

L.V.A., I.N.S.A. Bat 303, Villeurbanne, France

Jean Louis Guyader

Institut National des Sciences Appliquees, 69621 Villeurbanne Cedex, France

Inspired by precedent studies on the possibility of writing simple differential equations governing the evolution of vibratory energy density [D. J. Nefske and S. H. Sung, Trans. ASME 111, 94--100 (1989)], and equation of diffusion and its related conditions at discontinuities have been developed for an energetic quantity (Omega) in the case of flexural waves propagating in beams, where (Omega) represents the space-averaged far-field part of the displacement autospectrum, is proportional to energy density, but does not need extra time averaging. Several assumptions based on frequency and space averaging allow writing energetic conditions at discontinuities and defining a complete formalism for monodimensional problems. The procedure is applied to two coupled Euler Bernoulli beams: (Omega) is numerically in very good agreement with ``exact'' space and frequency-averaged far-field results and so the conditions at discontinuities are validated. Knowing that (Omega) allows for the ability to obtain an approximation of the energy flow in the beams and so gives an idea of how the energy propagates in the structure. These good results are encouraging, but the generalization of the procedure to plates is not trivial and requires further assumptions.