Modal identification in the case of complex modes : use of the wavelet analysis applied to the after-shock responses of a masonry wall during shear compression tests

In real structures, the proportional damping assumption is never strictly verified. Indexes of non-proportionality are then necessary to determine if this assumption leading to real modes still remains valid. If not, complex modes will appear and moreover, if their corresponding natural frequencies are close, their imaginary part can become large. In this paper, a new non-proportionality index, quantifying the ‘‘complexity” of mode shapes, is presented, derived from the notion of optimal complex modes introduced by Adhikari. This new index is designed for experimental results, for which the system’s parameters are not known, and proven to be equal to the previous one up to the first order on damping. Modal identification based on wavelet analysis is considered promising in this study for processing free responses of non-proportionally damped systems, integrated in noise, to directly obtain complex modes. A procedure for choosing an appropriate quality factor for the time-frequency resolution, necessary to get correct identification results in the case of free responses combined with responses to ambient excitation and/or to additive noise, is detailed. The proposed identification technique based on Continuous Wavelet Transform (CWT) is finally applied on different transient responses of a masonry wall specimen during an experimental campaign comprising simultaneous vibrations and shear-compression tests. The results of the CWT method for modal identification are compared with those obtained by a classical modal analysis technique, called Least Squares Complex Frequency method, by means of the Modal Assurance Criterion and the proposed nonproportionality index.