Vibration Analysis of Cracked Beam

Cracks in vibrating component can initiate catastrophic failures. The presences of cracks change the physical characteristics of a structure which in turn alter its dynamic response characteristics. Therefore there is need to understand dynamics of cracked structures. Crack depth and location are the main parameters for the vibration analysis. So it becomes very important to monitor the changes in the response parameters of the structure to access structural integrity, performance and safety. To examine the effect of the crack to the natural frequency of beams. In the present study, vibration analysis is carried out on a cantilever beam with two open transverse cracks, to study the response characteristics. In first phase local compliance matrices of different degree of freedom have been used model transverse cracks in beam on available expression of stress intensity factors and the associated expressions for strain energy release rates. Suitable boundary condition are used to find out natural frequency and mode shapes. The results obtained numerically are validated with the results obtained from the simulation. The simulations have done with the help of ANSYS software. A neural network for the cracked structure is trained to approximate the response of the structure by the data set prepared for various crack sizes and locations. Feed-forward multilayer neural networks trained by back-propagation are used to learn the input (the location and depth of a crack)-output (the structural eigenfrequencies) relation of the structural system. With this trained neural network minimizing the difference from the measured frequencies. It is verified from both computational and simulation analysis that the presence of crack decreases the natural frequency of vibration. The mode shapes also changes considerably due to the presence of crack.

[1]  A. S. Sekhar,et al.  Model-based identification of two cracks in a rotor system , 2004 .

[2]  Sadettin Orhan Analysis of free and forced vibration of a cracked cantilever beam , 2007 .

[3]  H. Y. Hwang,et al.  Damage detection in structures using a few frequency response measurements , 2004 .

[4]  H. Nahvi,et al.  Crack detection in beams using experimental modal data and finite element model , 2005 .

[5]  A. S. J. Swamidas,et al.  Crack identification in vibrating beams using the energy method , 2001 .

[6]  Nikos A. Aspragathos,et al.  Identification of crack location and magnitude in a cantilever beam from the vibration modes , 1990 .

[7]  Sundaram Suresh,et al.  Identification of crack location and depth in a cantilever beam using a modular neural network approach , 2004 .

[8]  Athanasios Chasalevris,et al.  Identification of multiple cracks in beams under bending , 2006 .

[9]  D. S. Dugdale,et al.  Introduction to the Mechanics of Solids , 1967 .

[10]  S. Loutridis,et al.  Forced vibration behaviour and crack detection of cracked beams using instantaneous frequency , 2005 .

[11]  Amiya R Mohanty,et al.  Vibrations of cracked rotor system: transverse crack versus slant crack , 2005 .

[12]  S. K. Maiti,et al.  Experimental verification of a method of detection of multiple cracks in beams based on frequency measurements , 2005 .

[13]  Baris Binici,et al.  Vibration of beams with multiple open cracks subjected to axial force , 2005 .

[14]  P. C. Paris,et al.  The Stress Analysis of Cracks Handbook, Third Edition , 2000 .

[15]  C. Navarro,et al.  APPROXIMATE CALCULATION OF THE FUNDAMENTAL FREQUENCY FOR BENDING VIBRATIONS OF CRACKED BEAMS , 1999 .

[16]  H. Yoon,et al.  Free vibration analysis of Euler-Bernoulli beam with double cracks , 2007 .

[17]  A. Trochidis,et al.  A method for determining the location and depth of cracks in double-cracked beams , 2004 .

[18]  Rajiv Tiwari,et al.  Identification of an open crack model in a beam based on force–response measurements , 2004 .

[19]  Andrew D. Dimarogonas,et al.  A CONTINUOUS CRACKED BEAM VIBRATION THEORY , 1998 .

[20]  R. A. Shenoi,et al.  Quantification and localisation of damage in beam-like structures by using artificial neural networks with experimental validation , 2003 .

[21]  R. Ruotolo,et al.  Harmonic analysis of the vibrations of a cantilevered beam with a closing crack , 1996 .

[22]  Myung-Won Suh,et al.  Crack Identification Using Hybrid Neuro-Genetic Technique , 2000 .

[23]  X. Fang,et al.  Structural damage detection using neural network with learning rate improvement , 2005 .

[24]  D. Y. Zheng,et al.  Free vibration analysis of a cracked beam by finite element method , 2004 .

[25]  M. Kısa,et al.  THE EFFECTS OF CLOSURE OF CRACKS ON THE DYNAMICS OF A CRACKED CANTILEVER BEAM , 2000 .

[26]  C. A. Papadopoulos,et al.  Crack identification in rotating shafts by coupled response measurements , 2002 .

[27]  J. M. Chandra Kishen,et al.  Finite element analysis for fracture behavior of cracked beam-columns , 2004 .

[28]  Kshitij Gupta,et al.  Dynamics of a two-crack rotor , 2003 .

[29]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[30]  S. K. Maiti,et al.  Detection of multiple cracks using frequency measurements , 2003 .