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Change in mode shape nodes of multiple cracked bar: I. The theoretical study

In present paper change in position of mode shape nodes induced by multiple cracks in bar is studied with purpose to use for the multiple crack detection from measured mode shape nodes. First, there is derived an explicit expression for natural modes in axial vibration of multiple cracked bar that allows obtaining exact positions of the node in the case of single and double crack. | Volume 35 Number 3 3 Vietnam Journal of Mechanics, VAST, Vol. 35, No. 3 (2013), pp. 175 – 188 CHANGE IN MODE SHAPE NODES OF MULTIPLE CRACKED BAR: I. THE THEORETICAL STUDY N. T. Khiem∗ , L. K. Toan, N. T. L. Khue Institute of Mechanics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam ∗ E-mail: ntkhiem@imech.ac.vn Abstract. In present paper change in position of mode shape nodes induced by multiple cracks in bar is studied with purpose to use for the multiple crack detection from measured mode shape nodes. First, there is derived an explicit expression for natural modes in axial vibration of multiple cracked bar that allows obtaining exact positions of the node in the case of single and double crack. The change in mode shape nodes induced by multiple cracks provides an important indicator for crack localization in bar. Finally, a procedure for multiple crack detection by using mode shape nodes has been proposed and examined in an example of application. Keywords: Multiple cracked bar, crack detection, mode shape nodes, vibration method, modal analysis. 1. INTRODUCTION The damage detection problem in structure has received recently a great research interest and the vibration-based approach to solution of the problem has been proved to be the most efficient and promising. Numerous ideas were proposed and a lot of results has been obtained regarding to the problem as can be found in the comprehensive surveys given in [1-4], but it so far faces the unsolved difficulties associated mainly with the erroneousness of measured data and the lack of information on current structure configuration. Until a total solution of the difficulties has been found the best choice is to make use additionally the unemployed attributes of structure that are more sensitive to damage and less contaminated by noise for the damage diagnosis. The features frequently used as the diagnostic tool for the damage detection problem consist mostly of the dynamical characteristics of structure such as .