Characterizing hysteretic materials in complex systems from vibration measurements

A new method is proposed for estimating the material properties of a component in a complex system, given vibration measurements taken at points on the system. The method begins by identifying a set of unknown material parameters for each material. A finite element model is constructed using initial estimates of these parameters. A set of error metrics is defined and each metric is assumed to be zero when the correct parameters are used in the model. These error metrics may, for example, include averages of vibrational responses or modal properties. By evaluating the finite element model as the material parameters are varied, relationships between the material parameters and the error metrics are established. The best estimates of the material parameters are found by requiring that all error metrics be zero. The method is particularly valuable when applied to the in situ determination of hysteretic material properties, in which the frequency-dependent constitutive law might contain several unknown parameters. Examples will be presented that illustrate the accuracy and robustness of the method.