THE PROBLEM OF VIBRATION FIELD RECONSTRUCTION: STATEMENT AND GENERAL PROPERTIES

The paper addresses the problem of reconstructing the vibration field of a structure or the acoustic field of a bounded fluid from limited data. The problem relates to practical situations when there is a need to know the dynamic stress and displacement distribution over the entire structure, e.g., for estimating its remaining service life, but the vibration may be measured only on accessible parts of the structure surface. In the paper, this problem is mathematically formulated and its general properties—solvability, uniqueness, and continuity are studied. Most attention is paid to the analysis of the error of reconstruction. One of the main results obtained is the proof of existence of the optimal vibration model of the structure,which renders minimum to the reconstruction error. The application of the results to discrete systems is discussed.