Identification of a Global Model Describing the Tempera- ture Effects on the Dynamics of a Smart Composite Beam J.D. Hios, S.D. Fassois ∗ Stochastic Mechanical Systems and Automation (SMSA) Laboratory, Department of Mechanical & Aeronautical Engineering, University of Patras, GR 265 00 Patras, Greece E-mail: {hiosj, fassois}@mech.upatras.gr Internet: http://www.mech.upatras.gr/∼sms Abstract The identification of a global model describing the dynamics of a smart composite beam under various tem- peratures is addressed. The problem is treated within a novel Statistical Functional Pooling Framework featuring global, stochastic Functionally Pooled (FP) models with explicit functional dependence on temper- ature. This framework circumvents the disadvantages associated with conventional multi-model approaches in which a customary model is identified for each temperature, with no explicit dependence on temperature being directly provided. In addition it offers a compact global model and optimal statistical accuracy. A global Functionally Pooled Vector AutoRegressive with eXogenous excitation model (FP-VARX model) de- scribing the dynamics of the considered beam is then identified using experimental data records. Its analysis indicates that the beam’s natural frequencies decrease with increasing temperature in a somewhat nonlinear or approximately linear fashion, while the dependence on temperature seems weaker, but of potentially more complicated nature, for the damping factors. The global model characteristics are confirmed as being in good agreement with those obtained by conventional multi-model analysis. 1 Introduction The increased demands of modern engineering applications for high performance and safety has underscored the importance of understanding the way environmental factors (such as temperature or humidity) affect the dynamics of a structure. This knowledge is valuable as it may be used for design purposes, the updating of analytical models, and in damage detection. A considerable amount of effort has been devoted to investigating the variability of the modal parameters of large civil structures, such as bridges, due to environmental effects. Several studies have shown that environ- mental factors – most notably temperature – cause significant changes, especially in modal frequencies. As a result, there has been a growing interest in developing quantitative relationships between frequencies and temperatures. In Sohn et al. [1] a concrete highway bridge is studied in the frequency range of [0, 50] Hz , and it is found that the variation of the first two modes is around 5% over a 24-hour time period, with temperatures varying within [20, 45] o C . In order to establish a relationship between the structure’s modal frequencies and temperature, impact excitation data are transformed in the frequency domain to obtain the structural modes, whereas at the same time temperature measurements are obtained at different locations on the structure. The data collected indicate a decreasing trend of the modal frequencies with increasing temperature. The frequencies are thereafter associated with the temporal and spatial temperature profile of the structure by * Corresponding author. ISMA 2006 International Conference on NOISE and VIBRATION Engineering September 18-20, 2006 Katholieke Universiteit Leuven, Belgium