Identification of civil structures with nonproportional damping

Recently, the method of Hilbert transform has been used successfully by the authors to identify parameters of linear structures with real eigenvalues and eigenvectors, e.g., structures with proportional damping. Frequently, linear structures may not have proportional damping so that normal modes do not exist. In this case, all the eigenvalues, eigenvectors and modeshapes are complex. In this paper, the Hilbert transform and the method of Empirical Mode Decomposition are used to identify the parameters of structures with nonproportional damping using the impulse response data. Measured impulse response signals are first decomposed into Intrinsic Mode Functions using the method of Empirical Mode Decomposition with intermittency criteria. An Intrinsic Mode Function (IMF) contains only one characteristic time scale (frequency), which may involve the contribution of a complex conjugate pair of modes with a unique frequency and a damping ratio, referred to as the modal response. It is shown that all the modal responses can be obtained from IMFs. Then, each modal response is decomposed in the frequency-time domain to yield instantaneous phase angle and amplitude as functions of time using the Hilbert transform. Based on only a single measurement of the impulse response time history at one location, the complex eigenvalues of the linear structure can be identified using a simple analysis procedure. When the response time histories are measured at all locations, the proposed methodology is capable of identifying the complex modeshapes as well as the mass, damping and stiffness matrices of the structure. The effectiveness and accuracy of the methodology presented are demonstrated through numerical simulations. It is shown that complete dynamic characteristics of linear structures with nonproportional damping can be identified effectively using the Hilbert transform and the Empirical Mode Decomposition method.