On crack detection in curved beams using change of natural frequency

In this study, an inverse method for the purpose of identifying the parameters of a single-edge crack in a curved beam is investigated. This method requires both numerical and experimental natural frequencies. The differential quadrature element method (DQEM) is introduced to get the numerical ones. For the purpose of implementing the DQEM the beam is divided into some elements and the governing equations, the continuity and the boundary conditions, are exerted on these elements to create an eigenvalue problem which is solved to obtain the required frequencies. A rotational spring whose stiffness is a function of crack depth is used to model the crack. An objective function with the variables of crack location and depth which is the weighted mean squared error between experimental and numerical frequencies is defined. The artificial bee colony algorithm (ABC) an optimization algorithm inspired by the natural foraging behavior of honeybees is used to minimize the aforementioned objective function and obtain crack parameters. To investigate the accuracy of this non-destructive, fast and easy method, an experimental modal analysis test is conducted on a cracked beam. The results indicate that the position and depth of the crack can be determined successfully using this method. This test is done five times with a different crack depth each time, to show the efficiency of the method for all cracks even small ones. A brief investigation is also done on the effect of crack location and depth on the natural frequencies.

[1]  S. M. Seyedpoor,et al.  A new damage detection indicator for beams based on mode shape data , 2015 .

[2]  Marta B. Rosales,et al.  Crack detection in beam-like structures , 2009 .

[3]  Xianyue Su,et al.  Damage detection method in complicated beams with varying flexural stiffness , 2011 .

[4]  D. Karaboga,et al.  On the performance of artificial bee colony (ABC) algorithm , 2008, Appl. Soft Comput..

[5]  Saeed Shojaee,et al.  A direct damage detection method using Multiple Damage Localization Index Based on Mode Shapes criterion , 2014 .

[6]  José Fernández-Sáez,et al.  Unique determination of a single crack in a uniform simply supported beam in bending vibration , 2016 .

[7]  Chang-New Chen.  DQEM analysis of in-plane vibration of curved beam structures , 2005, Adv. Eng. Softw..

[8]  M. S. Issa,et al.  Extensional vibrations of continuous circular curved beams with rotary inertia and shear deformation. II: Forced vibration , 1987 .

[9]  Songye Zhu,et al.  Adaptive-scale damage detection strategy for plate structures based on wavelet finite element model , 2015 .

[10]  S. Olutunde Oyadiji,et al.  Single and Multiple Crack Detection in Simply-Supported Beams Using SWT , 2015 .

[11]  Shuncong Zhong,et al.  Detection of cracks in simply-supported beams by continuous wavelet transform of reconstructed modal data , 2011 .

[12]  H. Srirangarajan,et al.  Detection of crack in L-shaped pipes filled with fluid based on transverse natural frequencies , 2005 .

[13]  H. R. Öz,et al.  In-Plane Vibrations of Circular Curved Beams with a Transverse Open Crack , 2006 .

[14]  Tommy H.T. Chan,et al.  An improved modal strain energy method for structural damagedetection, 2D simulation , 2015 .

[15]  H. J. Xu,et al.  Structural damage detection based on Chaotic Artificial Bee Colony algorithm , 2015 .

[16]  Giuseppe Ruta,et al.  Vibration and damage detection in undamaged and cracked circular arches: Experimental and analytical results , 2008 .

[17]  Mohsen Ghafory-Ashtiany,et al.  New Timoshenko-cracked beam element and crack detection in beam-like structures using genetic algorithm , 2014 .

[18]  Mustafa Sabuncu,et al.  Crack effects on the in-plane static and dynamic stabilities of a curved beam with an edge crack , 2011 .