Identification and applications of boundary effects in beams

Presented here is a signal decomposition method for extracting boundary effects from an operational deflection shape (ODS) of a structure under harmonic excitation. It decomposes an ODS into central and boundary solutions using a sliding-window least-squares curve-fitting technique, and the boundary solutions can be used to reveal damage locations, and the central solutions can be used to identify boundary conditions. Except an experimental ODS the method requires no model or historical data for comparison. Exact mode shapes and ODSs of beams with damage are obtained by spectral element analysis. Boundary and central solutions caused by different boundary conditions, different loading conditions, and different damage with or without noise are simulated and characterized. Numerical results show that Gibbs' phenomenon caused by the use of continuously differential functions to fit ODSs with discontinuous first-, second-, and/or third-order derivatives actually makes boundary solutions excellent damage indicators. Several experiments are performed using a scanning laser vibrometer for sensing and a lead zirconate titanate (PZT) patch for actuation. The experimental results confirm the feasibility and accuracy of this boundary effect detection method in detecting multiple defects and identifying boundary conditions of beams.