## Obiettivo

(1) A thorough literature survey of model updating techniques was conducted but no directly applicable methods were encountered. The bounds of modal analysis and updating procedures were also investigated. The controlling parameters of high frequency region dynamic behaviour were identified for using in updating algorithms.

(2) The model updating algorithm development at IC was done in two phases, separated by a further work package aiming at applying the methodology of the first phase to the industrial test cases: car muffler and rail system. The FE modelling and the vibration tests were done by the industrial partners and it was found that further testing and modelling effort was required in both cases.

(3) The initial application of the updating method on industrial models revealed a number of weaknesses that are common to most FRF-based methods, and FE model updating methods in general: the large size of the industrial FE models and the relatively small number of measurements.

(4) The updating methodology was improved via subs-structuring techniques, a q-value formulation and the introduction of new correlation functions. The vibration tests were repeated by the industrial partners and the second phase of the updating task was conducted, this time with more success.

(5) In any case, the ability of the updating methodology was demonstrated with simulated representative examples and the algorithms were incorporated into the FEMtools package by DDS.

(6) The developed force identification procedure uses displacement, velocity or acceleration measurements on the structure to identify nodal or distributed forces. The formulation includes a modal transformation and expansion of the test data to the full set of DOFs of the FE model. In many cases, it is possible to reduce the number of forces by linking force components into a lower number of forces or to use a force model and select the variables in the model as updating parameters. If not, it may be more reliable to estimate the forces and use a force updating procedure, only allowing adjustments of the force estimates within given constraints. Because such a situation is thought of as being rather exceptional, only the indirect identification method was implemented.

(7) The practical application of the force identification method to the two industrial cases has shown that it is an effective tool. Considering noisy test data, unknown damping, limitations of the FE model (no full modal correlation was obtained after FE model updating) and errors due to the modal truncation, it was shown that re-synthesis of the displacements at given frequencies using the identified forces, yields satisfactory correlation with the measured displacements.

(8) The project focused on one of the most advanced applications of acoustic analysis, which is the study of how acoustic performance can be optimally modified by changing the design parameters of a structure. It was found that the way to do this is to compute acoustic pressure sensitivity coefficients using the chain rule equation. This requires the multiplication of derivatives of sound pressure with respect to the boundary velocity (acoustic sensitivity) with the derivatives of the normal velocity with respect to a design variable (structural sensitivity).

(9) The automation of the analysis for muffler design was found to be extremely difficult because of the specific features of the product: steel inner parts in contact, gas flow, temperature effects, complex vibratory, interaction with other components. An experimental study was conducted and the effects of temperature and gas flow were ignored. The theoretical analyses were conducted in the case of a simple (empty) muffler. Significant success was obtained for defining a design methodology using FE model and force updating.

(10) The automatic updating of the rail system model using measured data has been difficult because of large model size and lack of initial correlation. It was decided to reduce the size of the FE model and adjust it manually. Good results were obtained using this approach.

(11) The acoustic calculations using both the initial and updated models of the wheel showed a difference of about 20 dB between the corresponding calculated acoustic powers. The same trend was observed experimentally, the updated model giving an estimate that is within 1.3 dB of the measured values. This demonstrates the benefit of successful model updating.

(12) The algorithms developed during the project were incorporated into DDS software FEMtools which is sold commercially.

The project aims at improving design methods for products with respect to quality, reliability, durability and safety. This improvement will be achieved by integrating test results in the general design procedure. Test results will be used to validate the mathematical structural model, to validate the dynamic forces acting on the structure model and to compute the acoustical sensitivities to structural parameter changes. The updated and validated mathematical models will then be used with greater confidence in classical fatigue analysis and life time prediction programs.

The main tasks to achieve this goal are then :

1. Development of techniques for finite element model improvement using experimental test results.

2. Development of an iterative technique for updating the dynamic forces, based upon the use of sensitivities.

3. Computation of the structural sensitivity values based upon the use of the improved mathematical model. Computation of the acoustical sensitivity values based upon the use of the structural sensitivity values and of the measured or computed exterior noise reduction.

4. Demonstration of the developed design techniques on an industrial example, the design of a muffler with emphasis on exterior noise reduction (acoustic finite/boundary elements).

5. Demonstration of the developed design techniques on an industrial example : the design of a rail fastening system with emphasis on exterior noise reduction (statistical energy approach).

Since it is important to integrate these new design tools in existing hardware and software, they will be interfaced with three widely used finite element codes : SYSTUS, ANSYS and MSC/NASTRAN.

### Campo scientifico

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Data not available### Meccanismo di finanziamento

CSC - Cost-sharing contracts### Coordinatore

3001 HEVERLEE

Belgio