A local correspondence principle for mode shapes in structural dynamics

• A principle is introduced relating mode shapes from a model with mode shapes from an experiment.
• Experimental mode shapes can be accurately approximated using a limited number of FE modes.
• Included FE mode shapes belong only to a mode shape cluster around the corresponding FE mode.
• The approximation can be used to accurately expand experimental mode shape to full size.
• The approximation can be used to reduce noise on experimental mode shape estimates.

It is well known that experimentally obtained mode shapes can be smoothed by using a linear combination of mode shapes from a finite element (FE) model. This is known from the theory of structural modification (SM) and from the system equivalent reduction expansion process (SEREP). Using this approach the set of FE mode shapes to be included in the smoothing must be chosen a priori and the quality of the smoothing and a subsequent mode shape expansion depend significantly on this choice. The present paper provides a solution to the problem of choosing which mode shapes are the most important for the smoothing and how many of the mode shapes should be included in order to obtain an optimal solution. It is shown based on the classical sensitivity theory that for each experimental mode shape, a mode shape cluster can be defined for the mode shapes of the FE model that defines an optimal choice for the smoothing set. The sequence of FE mode shapes to be included in this mode shape cluster is prescribed by a simple principle denoted the principle of local correspondence (LC) the name referring to the fact that an experimentally obtained mode shape should not be considered as corresponding to a single FE mode shape, but rather as corresponding to the mentioned mode shape cluster. A test case for a steel plate is considered where the experimentally obtained mode shapes are smoothed using SEREP (using a fixed set of mode shapes) and using the LC principle, and it is shown that the LC principle secures a high quality of the smoothing whereas the SEREP provides results that are strongly dependent upon the actual choice of the included FE mode shapes and on the degrees of freedom included in the fitting set.