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A simplified frequency equation and its approximate solution of a beam with an incipient crack from a wave perspective |
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| Institution: | 1. School of Electronics and Computer Science, University of Southampton, Southampton, SO17 1BJ, UK;2. Department of Networked Systems and Services, Budapest University of Technology and Economics, Budapest, H-1117, Hungary;3. MTA-BME Information Systems Research Group, Hungarian Academy of Sciences, Budapest, H-1051, Hungary;1. Division of Gynecologic Oncology, Department of Obstetrics and Gynecology, Weill Cornell Medical College, New York-Presbyterian Hospital, New York, NY, United States;2. Department of Pathology, Weill Cornell Medical College, New York-Presbyterian Hospital, New York, NY, United States;3. Division of Hematology/Oncology, Department of Internal Medicine, University of Michigan, Ann Arbor, MI, United States |
| Abstract: | 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. |
| Keywords: | Beam Incipient crack Frequency equation Modal frequency Wave perspective Structural health monitoring |
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