Proportional flexibility matrix of structures

For cases of ambient vibration, in which excitations are unknown, the flexibility matrix is unavailable. In this study the Proportional Flexibility Matrix (PFM) is proposed, which is within a scalar to the true flexibility matrix. For the cases of complete and incomplete measured degrees of freedom, algorithms for assembling the PFM are presented, and the scalar multiplier between the PFM and real flexibility is approximately shown to be the first modal mass. The proposed algorithm is examined by two numerical examples. With the application PFMs, the flexibility based damage detection methods developed previously can be implemented in ambient vibration.