A single pair-of-sensors technique for geometry consistent sensing of acceleration vector fields in beam structures: damage detection and dissipation estimation by POD modes

The acceleration vector field developed in a beam-like elastic structure is sampled over the space–time domain by a tri-axial accelerometer relocated over the beam surface while triggered by another mono-axial accelerometer fixed in space to attain synchronism. This technique leads to structure-geometry consistent spatio-temporal measurements of coupled structural dynamics. This result is established by extracting and interpreting the physics hidden in geometry consistent raw databases (mined by sweeping a single pair-of-sensors) with advanced proper orthogonal decomposition (POD) tools. For in-plane coupled vibrations, the dominant POD modes coincide with certain nonlinear normal modes of vibration belonging to the slow dynamics manifold structure. A parametric study reveals that they remain robust for increasing energy levels (nonlinearity) and changes in beam length-curvature (nonlinear geometry); and for out-of-plane bending and torsion vibration perturbations. Spatial local damage signatures due to a local mass and a plasticity defect are extracted from comparing logarithmically the POD modal shapes of healthy and damaged curved beams. In the presence of a local plasticity defect, certain dominant POD modes increases their internal dissipation index, the latter being modes independent for the healthy beam. This limited-sensor sensing technique is potentially useful for test and evaluation analysis of beam and cable like structural systems with complex geometries.