Resonant and antiresonant frequencies of multiple cracked bar
Author affiliations
DOI:
https://doi.org/10.15625/0866-7136/13092Keywords:
multi-cracked bar, longitudinal vibration, frequency equation, antiresonant frequencyAbstract
The natural frequencies or related resonant frequencies have been widely used for crack detection in structures by the vibration-based technique. However, antiresonant frequencies, the zeros of frequency response function, are less involved to use for the problem because they have not been thoroughly studied. The present paper addresses analysis of antiresonant frequencies of multiple cracked bar in comparison with the resonant ones. First, exact characteristic equations for the resonant and antiresonant frequencies of bar with arbitrary number of cracks are conducted in a new form that is explicitly expressed in term of crack severities. Then, the conducted equations are employed for analysis of variation of resonant and antiresonant frequencies versus crack position and depth. Numerical results show that antiresonant frequencies are indeed useful indicators for crack detection in bar mutually with the resonant ones.
Downloads
References
R. D. Adams, P. Cawley, C. J. Pye, and B. J. Stone. A vibration technique for non-destructively assessing the integrity of structures. Journal of Mechanical Engineering Science, 20, (2), (1978), pp. 93–100. https://doi.org/10.1243/jmes_jour_1978_020_016_02.
Y. Narkis. Identification of crack location in vibrating simply supported beams. Journal of Sound and Vibration, 172, (4), (1994), pp. 549–558. https://doi.org/10.1006/jsvi.1994.1195.
A. Morassi. Identification of a crack in a rod based on changes in a pair of natural frequencies. Journal of Sound and Vibration, 242, (4), (2001), pp. 577–596. https://doi.org/10.1006/jsvi.2000.3380.
M. Dilena and A. Morassi. Detecting cracks in a longitudinally vibrating beam with dissipative boundary conditions. Journal of Sound and Vibration, 267, (1), (2003), pp. 87–103. https://doi.org/10.1016/s0022-460x(03)00176-7.
R. Ruotolo and C. Surace. Natural frequencies of a bar with multiple cracks. Journal of Sound and Vibration, 272, (1-2), (2004), pp. 301–316. https://doi.org/10.1016/s0022-460x(03)00761-2.
L. Rubio, J. Fernández-Sáez, and A. Morassi. Identification of two cracks in a rod by minimal resonant and antiresonant frequency data. Mechanical Systems and Signal Processing, 60, (2015), pp. 1–13. https://doi.org/10.1016/j.ymssp.2015.01.025.
E. I. Shifrin. Inverse spectral problem for a rod with multiple cracks. Mechanical Systems and Signal Processing, 56, (2015), pp. 181–196. https://doi.org/10.1016/j.ymssp.2014.11.004.
E. I. Shifrin. Identification of a finite number of small cracks in a rod using natural frequencies. Mechanical Systems and Signal Processing, 70, (2016), pp. 613–624. https://doi.org/10.1016/j.ymssp.2015.09.023.
L. Rubio, J. Fernández-Sáez, and A. Morassi. The full nonlinear crack detection problem in uniform vibrating rods. Journal of Sound and Vibration, 339, (2015), pp. 99–111. https://doi.org/10.1016/j.jsv.2014.11.011.
L. Rubio, J. Fernández-Sáez, and A. Morassi. Crack identification in non-uniform rods by two frequency data. International Journal of Solids and Structures, 75, (2015), pp. 61–80. https://doi.org/10.1016/j.ijsolstr.2015.08.001.
G. M. L. Gladwell and A. Morassi. Estimating damage in a rod from changes in node positions. Inverse Problems in Engineering, 7, (3), (1999), pp. 215–233. https://doi.org/10.1080/174159799088027695.
N. T. Khiem, L. K. Toan, and N. T. L. Khue. Change in mode shape nodes of multiple cracked bar: I. The theoretical study. Vietnam Journal of Mechanics, 35, (3), (2013), pp. 175–188. https://doi.org/10.15625/0866-7136/35/3/2486.
N. T. Khiem, L. K. Toan, and N. T. L. Khue. Change in mode shape nodes of multiple cracked bar: II. The numerical analysis. Vietnam Journal of Mechanics, 35, (4), (2013), pp. 299–311. https://doi.org/10.15625/0866-7136/35/4/2487.
N. T. Khiem, P. T. Hang, and L. K. Toan. Crack detection in pile by measurements of frequency response function. Nondestructive Testing and Evaluation, 31, (2), (2016), pp. 122–141. https://doi.org/10.1080/10589759.2015.1081904.
M. Dilena and A. Morassi. Structural health monitoring of rods based on natural frequency and antiresonant frequency measurements. Structural Health Monitoring, 8, (2), (2009), pp. 149–173. https://doi.org/10.1177/1475921708102103.
M. Dilena and A. Morassi. Reconstruction method for damage detection in beams based on natural frequency and antiresonant frequency measurements. Journal of Engineering Mechanics, 136, (3), (2010), pp. 329–344. https://doi.org/10.1061/(asce)0733-9399(2010)136:3(329).
L. Rubio, J. Fernández-Sáez, and A. Morassi. Identification of two cracks in a rod by minimal resonant and antiresonant frequency data. Mechanical Systems and Signal Processing, 60, (2015), pp. 1–13. https://doi.org/10.1016/j.ymssp.2015.01.025.
T. G. Chondros, A. D. Dimarogonas, and J. Yao. Longitudinal vibration of a continuous cracked bar. Engineering Fracture Mechanics, 61, (5-6), (1998), pp. 593–606. https://doi.org/10.1016/s0013-7944(98)00071-x.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
