Energy residual : a tool to study the dispersion of vibroacoustic performances of structures

Serial manufacturing of products is the reason why studies on uncertainties are becoming more and more important. For vibro-acoustic problems, structural uncertainties can induce hypersensitivity: very small structural variations will be responsible of large differences on radiated sound. Hypersensitive behavior has been observed on simple structures like beer cans as well as complicated one like cars. The analysis of plates networks show that connection angle controls vibration hypersensitivity. In addition, if an angle is responsible of hypersensitivity, dispersion of behavior is observed on each plate of the network. So, when structures "industrially identical" present large dispersion, one small structural zone can control the phenomenon. The detection of this zone is the goal of the present study. The proposed method relies first on the resolution of the nominal structure problem, that is to say the calculation of nominal vibration modes. Modified structure, in accordance with industrial variability, has a different equation of motion than the nominal one, consequently the introduction of nominal vibration modes into modified structure equation leads to residual efforts or displacements, which are used in terms of kinetic energy as an indicator. Its link with natural frequency bounds is demonstrated. Then the residual energy distribution over the structure is analyzed for plates network. The structural zone of maximum residual energy is seen to correspond to that of the angle responsible for hypersensitivity. An application on real car body is then studied. The model is based on F.E.M. and particular attention is paid to spot welding process. Structural zones are detected, where missing welding spots produce hypersensitivity