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This paper presents a simplified frequency equation and its approximate solution to predict the modal frequencies of a beam with an incipient crack. The physical implication of the simplified frequency equation is fully described from a wave perspective for the cracked beam with arbitrary support conditions. The approximate solution of the proposed frequency equation is derived from a wave perspective as well. The asymptotic equivalence is demonstrated between the approximate solution and that obtained by the first order perturbation method as the mode number increases. The validity of the proposed approach is demonstrated through comparison to both numerical results from finite element analysis and experimental data. [ABSTRACT FROM AUTHOR]

The sine-vibration-data-based model updating method plays an important role in improving the finite element modeling level in spacecraft engineering. The key to sine-vibration-data-based model updating method is the coherence of the modal frequencies and the response curves of the model before & after updated. Firstly, the analysis method of the structure response was derived based on the base excitation. Secondly, the updating method was studied in two steps, which makes the modal frequencies and the response curves of the analysis model consistent with that of the test model. Finally, the GARTURE truss model was used to validate the two step updating method. The results show that the fundamental frequencies of the analysis model agree with the test model, the first ten modal frequency error is under 0.15%, and the response peak error of the typical points is less than 1%. [ABSTRACT FROM AUTHOR]