Identification of Electromechanical Coupling in Piezo-Structures

An identification method based on a structural model updating procedure may be used to improve the knowledge of a piezoelectric tested structure and to determine the coupling coefficients of the piezoelectric material. This procedure starts with the modal analysis of the open-loop instrumented structure. Let the target modes be a subset of the model modes; a selection of sensor (generally accelerometers) locations is then performed by determining the smaller subset such that the H2 modal norm is as close as possible to the modal norm of the original full set. In most cases, experimental testing with the selected sensor set will give acceptable information to identify target modes. These data, coupled with electrical sensing at the piezoelectric element level, will then be used to perform modal analysis of the piezo-structure. A pole-residue development of the open-loop piezo-structure shows that conventional algorithms may be used to estimate the mechanical modal parameters and the electromechanical coupling matrix. The second step of the procedure is to perform model updating itself. The initial finite element piezoelectric model will be improved stiffness corrections to the global stiffness matrix.. The corrections are split in their mechanical and electromechanical contributions. It is then possible to separate mechanical modelling errors from electromechanical coupling errors. The problem becomes a classical model updating problem which may be solved using well established techniques. This will result not only in a model behaving like the measures, but also in an improved knowledge of the structure behaviour without loosing physical insight. From a numerical point of view, it will be shown that ill-conditioning inherent to the presence of piezoelectric elements presents some difficulties at different steps of the model correction procedure. A clamped-free plate instrumented with piezo-laminates is used to illustrate the model updating approach. The selection of measurement points, using the modal norm criteria, is also presented. Experimental identification data will then be used as inputs for the model correction procedure and the behaviour of the updated model will be compared with the initial model dynamics.