Advanced Modal Analysis of Geometry Consistent Experimental Space-Time Databases in Nonlinear Structural Dynamics

We present a study focusing on mining-processing of geometry consistent space-time databases of acceleration fields developed in freely vibrating long aluminum alloy beams. Vibration data mining is conducted by single triad of accelerometers: one fixed and the other two being relocated to cover the structure. The mined space-time databases are evaluated by an advanced modal analysis technique based on proper orthogonal decomposition tools to determine whether they qualify as a genuine measurement of the acceleration vector field resolved along space and time varying local coordinates furnished naturally by the deforming surface of the beam structure. Despite the fact that the dynamics are coupled three-dimensional and evolving in interacting slow-fast time scales, the shapes of the extracted proper orthogonal modes of the transverse component of the acceleration vector field sampled by the single triad of accelerometers are found to be qualitatively close to shapes of normal modes predicted by the Euler-Bernoulli linear beam model. The quantitative differences stem from the influence on vibration dynamics that the static deformation infers to. The sensing-measuring of the acceleration vector field with limited sensor resources exploits the geometric mechanics concepts of slow and fast invariant manifolds thus contributing to low cost practical structural dynamics experimental data.