Christian Soize - soize@onera.fr
Structural Dynamics and Coupled Systems Department
ONERA
BP 72
92322 Chatillon Cedex
France
Popular version of paper 4pPL1
Presented Thursday afternoon, 25 June, 1998
ICA/ASA '98, Seattle, WA
The methods and the numerical computer codes in structural acoustics for the prediction of noise emitted by structural vibration in all the audible low-, medium- and high-frequency band, play a very important role in the design and the conception of industrial products. These include acoustic pollution and passenger comfort in different areas such as airplanes, helicopters, automobiles, high-speed trains, naval structures, but also, some features related to high technologies, such as acoustic loads on a satellite during its launching or acoustic health of submarines, etc. These methods allow the design to be improved before construction and optimization with respect to the acoustical problems.
Today, it is recognized that Computational Structural Mechanics (CSM) and Statistical Energy Analysis (SEA) are efficient for structural-acoustic prediction in low- and high-frequency ranges respectively. The analysis of the medium-frequency range remains very difficult due to the role played by the structural complexity araising in industrial structures. This structural complexity is constituted by all the equipment units and secondary substructures which are attached to the master structure and which cannot be modeled using a deterministic approach because the details of them are unknown, or are not accurately known. Experimental results show that the presence of a structural complexity induces an ``apparent strong damping'' in the master structure in the medium-frequency range and possibly in the low-frequency range. The resonance morphology is strongly attenuated for the master structure. This phenomenon can be explained by the net transmitted power flowing from the master structure to the structural complexity.
In order to improve the modeling of complex structural-acoustic system in the medium-frequency range, a theory, called the Fuzzy Structure Theory, has been introduced by the author in 1985 and is always in progress.
In this theory, the structural complexity is called a fuzzy substructure because the details on them are unknown, or are not accurately known. This explains the choice of the word ``fuzzy'' which has nothing to do with the mathematical theory concerning fuzzy sets and fuzzy logic. Consequently, a fuzzy structure is defined as a master structure that is accessible to conventional deterministic modeling, coupled with fuzzy substructures which are not accessible to conventional deterministic modeling and for which a probabilistic model is used. This recent theory allows us to predict the modulus and phases of the master-structure displacement field and of the acoustic pressure field induced by the master structure vibration, taking into account the fuzzy substructures attached to the master structure.
A second important feature related to the medium-frequency range is the construction of reduced models in order to make the use of medium-frequency models efficient.
It is known that, for low-frequency dynamic analysis in structural dynamics and structural acoustics, reduced models are a very efficient tool for constructing the solution. For instance, these techniques correspond to the use of the normal modes associated with the lowest eigenfrequencies of the master structure and are called the modal reduction. The efficiency of this kind of reduced model is due to the small number of generalized dynamical degrees of freedom used in the representation.
The fundamental problem related to the construction of a reduced model in the medium-frequency range for general dissipative structural-dynamics and structural-acoustics systems has not been solved yet. Methods based on the use of the normal modes in the medium- and high-frequency ranges have been proposed, but these methods can only be used for simply shaped structures in a context of an analytical theory. A new general approach is proposed for constructing such a reduced model in the medium-frequency range. This method is based on the use of the eigenfunctions corresponding to the higest eigenvalues of an operator related to the mechanical energy of the dynamical system in each narrow medium-frequency band.