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

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.

Resonant and antiresonant frequencies of multiple cracked bar

“…As zeros of FRF, antiresonant frequencies of a multiple cracked bar are seeking as follows. General expression of FRF for multiple cracked bars has been obtained by Khiem et al [12,13] in the form…”

“…However, the study showed that unique solution of the crack detection cannot be found by using only natural frequencies. Some efforts have been made to solve the problem by encompassing other vibration characteristics such mode shapes [11][12][13] or frequency response function [14], but it was successful when antiresonant frequencies have been employed [15][16][17]. Nevertheless, using additionally the c 2019 Vietnam Academy of Science and Technology antiresonant frequencies for crack detection in bar enables to obtain unique solution of the crack detection problem only for free end bar.…”

Crack identification in multiple cracked beams made of functionally graded material by using stationary wavelet transform of mode shapes

“…Determination of dynamic characteristics of cracked FGM beam can be obtained by using analytical [3][4][5][6][7][8][9][10][11], Galerkin's semi-analytical [12], finite element method (FEM) and dynamic stiffness method (DSM). The FEM has been developed and employed for modal analysis and identification of FGM beams [13][14][15][16].…”