B-spline Shell Finite Element Updating by Means of Vibration Measurements

Abstract

Within the context of structural dynamics, Finite Element (FE) models are commonly used to predict the system response. Theoretically derived mathematical models may often be inaccurate, in particular when dealing with complex structures. Several papers on FE models based on B-spline shape functions have been published in recent years (Kagan & Fischer, 2000; Hughes et al, 2005). Some papers showed the superior accuracy of B-spline FE models compared with classic polynomial FE models, especially when dealing with vibration problems (Hughes et al, 2009). This result may be useful in applications such as FE updating. Estimated data from measurements on a real system, such as frequency response functions (FRFs) or modal parameters, can be used to update the FE model. Although there are many papers in the literature dealing with FE updating, several open problems still exist. Updating techniques employing modal data require a previous identification process that can introduce errors, exceeding the level of accuracy required to update FE models (D’ambrogio & Fregolent, 2000). The number of modal parameters employed can usually be smaller than that of the parameters involved in the updating process, resulting in ill-defined formulations that require the use of regularization methods (Friswell et al., 2001; Zapico et al.,2003). Moreover, correlations of analytical and experimental modes are commonly needed for mode shapes pairing. Compared with updating methods using modal parameters as input, methods using FRFs as input present several advantages (Esfandiari et al., 2009; Lin & Zhu, 2006), since several frequency data are available to set an over-determined system of equations, and no correlation analysis for mode pairing is necessary in general. Nevertheless there are some issues concerning the use of FRF residues, such as the number of measurement degrees of freedom (dofs), the selection of frequency data and the ill-conditioning of the resulting system of equations. In addition, common to many FRF updating techniques is the incompatibility between the measurement dofs and the FE model dofs. Such incompatibility is usually considered from a dof number point of view only, measured dofs being a subset of the FE dofs. Reduction or expansion techniques are a common way to treat this kind of incompatibility (Friswell & Mottershead, 1995). A more general approach should also take into account the adoption of different dofs in the two models. As a matter of result, the adoption of B-spline functions as shape functions in a FE