| Novel vibration analysis frameworks for elastic structures with a crack are presented. The vibration analysis of a cracked structure has important applications for vibration-based structural health monitoring and damage detection of complex structures. For example, changes in vibration frequencies and response shapes of a structure during its lifetime can be used to determine that a crack has formed as well as to identify the crack location. The challenge here is that a vibrating cracked structure features a nonlinearity caused by repetitive opening and closing of crack faces during vibration cycles. This hinders analysts from the application of traditional linear vibration analysis tools such as the modal analysis or harmonic response analysis, which have been the most common tools for accurately predicting the vibration response of various types of mechanical and aerospace structures. As a consequence, the dynamic response of such a structure is not very well understood. Therefore, from both theoretical and practical standpoints, an efficient and accurate nonlinear vibration analysis framework for cracked structures is highly desirable.;There are two main goals of this research: (1) understanding the fundamental aspects of the nonlinear dynamics of cracked structures, with special attention to turbomachinery rotors with a cracked blade; and (2) exploiting the key findings for the development of efficient and accurate vibration analysis frameworks for such structures. The main contributions of this work are summarized as follows. First, a vibration analysis framework for a rotating cracked blade is developed based on the finite element method, component mode synthesis, and the harmonic-balance-based nonlinear forced response analysis. Key aspects of the vibration response of such a structure are examined. Second, the analysis framework is generalized for the analysis of a turbomachinery rotor with a cracked blade, and the effects of a cracked blade on a system-level vibration response are examined. Third, based on the key findings from these analyses, a new resonant-frequency-approximation method is proposed, and its applicability to various cases is discussed. Finally, a novel reduced-order modeling technique for cracked structures is introduced, for further expanding the applicability of the analysis framework presented in this study. |
