Engineering Transactions, 49, 4, pp. 485–510, 2001

Direct Stiffness Energy Model for a One-Dimensional Complex System

M.N. Ichchou
Laboratoire de Tribologie et Dynamique des Systemes Ecole Centrale de Lyon
France

L. Jezequel
Laboratoire de Tribologie et Dynamique des Systemes Ecole Centrale de Lyon
France

This paper deals with the high frequency analysis of one-dimensional waveguides. In this frequency range, this paper proposes a numerical implementation and tests of an alternative to the classical predictive dynamical methods. The originality of this approach consists in the fact that it is solely an energy density description. A numerical scheme very similar to the well-known direct stiffness method is employed here. This leads to a numerical code capable of predicting the mean value energy density for complex beam-like structure up to high frequencies. A twenty four components plane truss, including both the bending and extension motion is used as a verification test, and shows the ability of the proposed code to predict the high frequency dynamics of complex beam-like structures.
Full Text: PDF

References

F.J. FAHY, L'analyse statistique énergétique, Revue d'Acoustique, 33, 10–25, 1975.

S.A. RYBAK, V.D. BELOV, and B.D. TARTAKOVSKII, Propagation of vibrational energy in absorbing structures, Soviet Physical Acoustic, 23, 115–119, 1977.

D.J. NEFSKE and S.H. SUNG, Power flow finite element analysis of dynamic systems: basic theory and application to beams, NCA Publication, 3, 1987.

J.C. WOHLEVER and R.J. BERNHARD, Mechanical energy flow models of rods and beams, Journal of Sound and Vibration, 153, 1–19, 1992.

R.J. BERNHARD, O. BOUTHIER and J.C. WOHLEVER, Energy and structural intensity formulations of beam and plate vibrations, 3rd International Congress on Intensity, Senlis, France, 1990.

O.M. BOUTHIER and R.J. BERNHARD, Simple models of energy flow in vibrating membranes, Journal of Sound and Vibration, 182, 129–147, 1995.

O.M. BOUTHIER and R.J. BERNHARD, Simple models of energy flow in vibrating plates, Journal of Sound and Vibration, 182, 149–164, 1995.

M.N. ICHCHOU, A. LE BOT and L. JEZEQUEL, Energy models of one-dimensional multi-propagative systems, Journal of Sound and Vibration, 201, 535–554, 1997.

A. LE BOT, M.N. ICHCHOU and L. JEZEQUEL, Energy flow analysis for curved beams, Journal of the Acoustical Society of America, 102, 943–954, 1997.

M.N. ICHCHOU, A. LE BOT and L. JEZEQUEL, Radial and tangential energy flow models for curved wave guides, Vibration and Noise 95, 718–727, Venice, Italy, 1995.

M.N. ICHCHOU, A. LE BOT and L. JEZEQUEL, Beam network analysis by a power flow method, Transaction of ASME conference 95, 823–827, USA, Boston 1995.

Y. LASE, M.N. ICHCHOU and L. JEZEQUEL, Energy analysis of bars an beams: theoretical formulations, Journal of Sound and Vibration, 192, 281–305, 1996.

A. GIRARD and DEFOSSE, Frequency response smoothing, matrix assembly and structural paths: a new approach for structural dynamics up to high frequencies, Journal of Sound and Vibration, 137, 53–68, 1990.

R. AQUILINA, D. BONDOUX, and J. M. PAROT, Structural broad band fields in beam networks by a vibratory rays model, 3rd International Congress on Intensity, 85–94, Senlis, Prance, 1990.

L. BRILLOUIN, Wave propagation in periodic structures, Dover Publications, Inc., New York 1953.

M. DJIMADOUM and J.L. GUYADER, Possibilities to generalize the heat transfer approach to vibration of plates problems, Inter-Noise '95, CA, Newport Beach 1995.

B.R. MACE, On the statistical energy analysis hypothesis of coupling power proportionality and some implications of its failure, Journal of Sound and Vibration, 178, 95–112, 1994.

R.S. LANGLEY, Analysis of beam and plate vibrations by using the wave equation, Journal of Sound and Vibration, 150, 47–65, 1991.

R.S. LANGLEY, A wave intensity technique for the analysis of high frequency vibrations, Journal of Sound and Vibration, 159, 483–502, 1992.

R.S. LANGLEY, On the vibrational conductivity approach to high frequency dynamics for two–dimensional structural components, Journal of Sound and Vibration, 182, 637–657, 1995.

P.E. CHO, Energy flow analysis of coupled structures, Purdue University, PHD thesis, 1993.

P.E. CHO and R. J. BERNHARD, A simple method for predicting the energy flow distributions in frame structures, 3rd International Congress on Intensity, 347–354, Senlis, France 1990.

B.R. MACE, Power flow between two continuous one-dimensional subsystems: a wave solution, Journal of Sound and Vibration, 154, 289–319, 1992.

B.R. MACE, Power flow between two coupled beams, Journal of Sound and Vibration, 159, 305–325, 1992.

R. S. LANGLEY, Application of the dynamic stiffnes method to the free and forced vibrations of aircraft panels, Journal of Sound and Vibration, 135, 319–339, 1989.




Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland