Mode Shape Expansion From Data-Based System Identification Procedures.

Abstract

In almost all cases, the experimental data set of a dynamical test is incomplete as the
measurements are taken at selected locations in selected coordinate directions. This lack of measured
degrees of freedom can be solved in two ways, either by reducing the finite element model to the size
of experimental one or by expanding the experimental data to include the unmeasured degrees of
freedom in the finite element model. In this sense, mode shape expansion techniques deal with the
spatial incompatibility linked to the measurement of mode shapes through a limited set of physical
sensors and their analytical prediction at a (larger) number of finite element (FE) degrees of freedom
(DOFs). In other words, expansion methods seek to estimate the motion at all DOFs of a finite element
model based on measured information (mode shapes or frequency response functions) and prior
information about the structure under test in the form of a reference finite element model. In essence,
the finite element model is used as a high order polynomial curve fitter to estimate the experimental
mode shapes at the deleted DOF, and in general, more confidence can be placed in the expanded
results by increasing the number of measurement points. This paper presents the behavior of two mode
shape expansion techniques when modal data are obtained from system identification procedures. A
dynamic test of a transmission line tower numerically, simulated by Fadel Miguel et al. (2006),
provided the initial values and it is shown that accuracy results are achieved if the identified
parameters are well correlated with the theoretical model.