Limited Experimental Displacement Data used for obtaining Full-Field Dynamic Stress Strain Information Pawan Pingle, Peter Avitabile Structural Dynamics and Acoustic Systems Laboratory University of Massachusetts Lowell One University Avenue Lowell, Massachusetts 01854 ABSTRACT Full field displacement and full-field dynamic stress-strain information has been shown to be estimated accurately from limited sets of data using an expansion algorithm through analytical simulations. Experimental data is collected and used for the dynamic expansion process to predict dynamic stress-strain for a candidate structure. Experimental measurements are obtained in a controlled study using an impact excitation technique. Displacement data at limited locations is collected using dynamic photogrammetry and digital image correlation techniques. The full-field expanded displacement data is compared and validated with a reference solution. This full-field displacement data is then used to identify the dynamic stress-strain to show the usefulness of the technique. NOMENCLATURE Symbols: ^ nX ` ` @ @ @ @ @ full set displacement vector ^ aX reduced set displacement vector > aM reduced mass matrix > nM expanded mass matrix > aK reduced stiffness matrix > nK expanded stiffness matrix > aU reduced shape matrix > @g aU generalized inverse of reduced shape matrix > @ nU expanded shape matrix > @T transformation matrix. > @ UT SEREP transformation matrix. > @ n REF reference data at all degrees of freedom (dofs) > @ a RTO real time operating data at measured dofs > @ n ERTO expanded real time operating data at all dofs INTRODUCTION Generally, a structure is designed for many loading conditions including fatigue. The structure is considered to be safe under a certain number of loading cycles. But there are certain transient events that are difficult to model. These transient events can severely limit the structure’s fatigue life such that the structure might fail in fatigue much below the expected designed life. Examples of such transient events could be sudden gust of wind on a turbine blade or a helicopter hardlanding or a barge striking a bridge. The main emphasis of this work is directed towards blade type structures but the techniques developed can be applied to a variety of different types of structures. Continuous or periodic monitoring is required to assure the health of such structures to understand the effect of these types of transient events. Typically, only a handful of sensors are available for the evaluation of these rare, short-term events. This limited data does not always provide the details necessary in order to determine the effects of the events that occur, especially in terms of the overall fatigue usage for the system. Generally, a finite element model may be available but use of this limited data does not lend itself to easily integrate into the identification of the dynamic stress and the dynamic strain. T. Proulx (ed.), Linking Models and Experiments, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series 5, 201 DOI 10.1007/978-1-4419-9305-2_14, © The Society for Experimental Mechanics, Inc. 2011
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