We perform Operational Modal Analysis (OMA) through Frequency Domain Decomposition (FDD) on a test structure using a high speed camera. Using optical flow algorithms, brightness changes due to displacements of a test structure under load are translated into displacement data. By using a mirror, a split image is generated that enables a stereoscopic view of the structure and thus 3D information can be extracted from the high speed video footage.This setup is used to determine the modal parameters of the structure, especially the mode shapes with high spatial resolution. The mirror that is used to gather a second point of view onto the image sensor enables a cost-efficient stereoscopic measurement compared to a two-camera setup. Moreover, it eliminates the need of synchronizing two separate signals. This is also why OMA is used instead of EMA: as no force signal needs to be recorded, we can perform a full-field modal analysis with inputs from only one single device.The results are evaluated taking into account the accuracy as well as the complexity of the setup of the 3D measurements compared to a setup using triaxial accelerometers.
Abstract. In this paper, time integration procedures are demonstrated and investigated for dual Craig-Bampton reduced systems. The dual Craig-Bampton method for the reduction and successive coupling of dynamic systems employs free interface vibration modes, attachment modes and rigid body modes to build the reduction bases of the substructures, but assembles the substructures using interface forces. Thereby, the interface kinematic conditions are transformed, allowing for incompatibilities associated with the equilibrium residual in the substructure. Hence, the eigenvalues of the reduced-order model are not guaranteed to be upper bounds for the unreduced system's eigenvalues. Furthermore, the dual Craig-Bampton reduced system will always have as many negative eigenvalues as interface coupling conditions. The reduced system is unstable, rendering a straightforward time integration of the dual Craig-Bampton reduced system impossible.The feasibility of a reliable time integration of dual Craig-Bampton reduced systems is demonstrated and investigated in detail. The unstable behavior when time-integrating such systems without further modifications is illustrated and two approaches to overcome this instability are suggested: on the one hand, a modal analysis of the reduced system is performed as a subsequent step to the dual Craig-Bampton reduction. Only modes corresponding to positive eigenvalues are thereby kept for transient analysis. This allows for a stable time integration. On the other hand, a modal interface reduction during the dual Craig-Bampton reduction process is performed and only interface modes corresponding to positive eigenvalues are kept. This makes the final reduced system also positive definite. The accuracy using these two approaches is demonstrated in examples with either different initial conditions or varying external periodic excitations.
Camera-based 3D displacement measurements are only possible when two different viewing angles of the respective measurement point are available. We earlier introduced a simplified 3D reconstruction algorithm for camera-mirror measurements where the mirror reflects the second view onto the camera sensor to eliminate the need for a second (costly) high speed camera. In this study, we concentrate on formulating guidelines on how to position the mirror with respect to the camera and the measured structure, the goal being to minimize errors arising in the 3D reconstruction procedure. The focus lies on the angle between the optical axes of both camera views. We hereby also take into account limitations in the experimental setup that the special cameramirror-setup brings with it. This study is conducted in terms of simulations using the animation software BLENDER as well as real experiments on a simple vibrating structure.
The dual Craig-Bampton method, a substructuring method that employs free interface normal modes, rigid body modes and attachment modes, yields reduced systems with negative eigenvalues making a stable time integration impossible. A way to overcome this problem through a subsequent modal reduction of dual Craig-Bampton reduced systems is presented and investigated by a simple numerical example. Furthermore, the beneficial effect of additional static modes in the systems' reduction bases is demonstrated.
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