Separation of closely spaced modes by combining complex envelope displacement analysis with method of generating intrinsic mode functions through filtering algorithm based on wavelet packet decomposition

One of the important issues in the system identification and the spectrum analysis is the frequency resolution, i.e., the capability of distinguishing between two or more closely spaced frequency components. In the modal identification by the empirical mode decomposition （EMD） method, because of the separating capability of the method, it is still a challenge to consistently and reliably identify the parameters of structures of which modes are not well separated. A new method is introduced to generate the intrin- sic mode functions （IMFs） through the filtering algorithm based on the wavelet packet decomposition （GIFWPD）. In this paper, it is demonstrated that the CIFWPD method alone has a good capability of separating close modes, even under the severe condition beyond the critical frequency ratio limit which makes it impossible to separate two closely spaced harmonics by the EMD method. However, the GIFWPD-only based method is impelled to use a very fine sampling frequency with consequent prohibitive computational costs. Therefore, in order to decrease the computational load by reducing the amount of samples and improve the effectiveness of separation by increasing the frequency ratio, the present paper uses a combination of the complex envelope displacement analysis （CEDA） and the GIFWPD method. For the validation, two examples from the previous works are taken to show the results obtained by the GIFWPD-only based method and by combining the CEDA with the GIFWPD method.

EXPLORATION OF SUBSTITUTION OF REPEATED MODE SUBSPACES FOR CLOSELY SPACED MODE SUBSPACES

A new quantitative concept is introduced in this paper, which may be used to facilitate the measurement of the controllability of a subspace similar to subspace controllability degree. Then the concrete form of the subspace controllability degree of a flexible structure is derived, and the errors of subspace controllability degree and dynamical response caused by the substitution of a repeated mode subspace for a closely spaced mode subspace are discussed. All the results show that this substitution is rational under some conditions.

Low order vibration control for structures with highly correlated close modes

For the problem posed by closely spaced modes, this paper defined the MCC (modal correlation criterion) to measure the degree of correlation between close modes. It was proved that structures with certain features tend to have closely clustered modes and the corresponding mode shapes highly correlated. With this understanding, the closed-form expressions for controllability and observability Grammians were adopted to analyze the impacts of actuator/sensor placement on the controllability/observability of highly correlated close modes. On this basis, the problem of actuator/sensor placement, when the optimization criterion is based on modal controllability/observability, was simplified. Moreover, the dimension of the control/measurement vector in independent modal space control for highly correlated close modes was proved to have the potential to be reduced, therefore fewer actuators and sensors were required in this dimension-reduced control strategy. Finally, the desirable vibration suppression for an example structure showed that the theory and methods of this paper were accurate and effective.