In this dissertation, a framework is developed and demonstrated for the use of a new shape measurement system consisting of fiber Bragg grating (FBG) based strain sensors, a shape determination algorithm based on Frenet frames, and a signal processing algorithm based on modal analysis techniques. The system is experimentally validated by using a long slender, aluminum cantilever structure (65.625"x2.0"x0.125") with eight serially multiplexed FBG sensors. The multiplexed FBG sensors measure the bending strain distribution along the cantilever structure, and this distribution is used to calculate the dynamic shape of the structure forced by a base excitation. The structural shape data is processed by using modal analysis techniques to determine the modal coefficients and the associated spatial modes that best represent the structure's vibration. The results obtained for the modal coefficients are found to compare well with results of Fourier transform analysis of signals recorded over time. Analysis by using the shape algorithm developed herein demonstrates the effectiveness of using a Frenet frame-based technique to determine the shape of the structure from recorded strain data. Sources of error due to factors such as the number of sensors and Taylor series approximation in the shape algorithm are examined.

The methodology discussed in this dissertation allows both static and dynamic monitoring of structural shape characteristics. This type of real-time analysis may be useful for applications in structural health monitoring where changes in the modal coefficients may lead to indications of damage to the structure and in applications such as sonar arrays and aircraft wings where knowledge of a structure's shape can yield improved results.