A New Reactive Hybrid Membership Function in Fuzzy Approach for Identification of Inclined Edge Crack in Cantilever Beam Using Vibration Signatures Ranjan K. Behera 1, a * , Sasmita Sahu 2, b , Dayal R. Parhi 3, c 1,2,3 Department of Mechanical Engineering, National Institute of Technology,Rourkela,Odisha, India a ranjancet@gmail.com, b gudusasmita@gmail.com, c dayalparhi@yahoo.com Keywords: inclined edge crack, crack parameters, FEA, vibration signatures, fuzzy, hybrid MF Abstract. In this paper, the crack identification using smart technique (by several hybrid membership functions in a fuzzy controller) has been developed for inverse analysis of the vibration signatures (like modal frequencies, mode shapes) and crack parameters (like crack depth, crack location and crack inclination) of an inclined edge crack cantilever beam. The modal frequencies are obtained from finite element (using ANSYS) and experimental analysis which are used as inputs to the hybrid fuzzy controller. The hybrid fuzzy system is designed by taking different types of membership functions (MF) to determine the crack parameters. The calculated first three modal frequencies are used to create number of fuzzy rules with the three output crack parameters. Finally, the proposed hybrid technique is validated by comparing the results obtained from trapezoidal and Gaussian fuzzy controllers, FEA and experimental results. The outcomes obtained from hybrid fuzzy controller are in good agreement with experimental results. Nomenclature L : Length of the cantilever beam ν : Poisson’s ratio b : Width of the cantilever beam E : Young's modulus of elasticity t : Thickness of the cantilever beam RFNF : Relative First Natural Frequency a : Edge Crack depth RSNF : Relative Second Natural Frequency L 1 : Crack location from fixed end RTNF : Relative Third Natural Frequency β : Relative crack location (= L 1 /L) RCL : Relative Crack Location α : Relative crack depth (= a /t) RCD : Relative Crack Depth θ : Crack inclination angle CA : Crack Angle Introduction Identification of premature cracks in engineering vibrating structure like beams, plates etc. during their life period is the key issue to the researchers. There are several techniques to evaluate the problem of a faulty beam such as theoretical, analytical, experimental etc. FEM (Finite Element Method) is a general method to get the stiffness matrix of the cracked beam element. Many researchers are using vibration parameters like stiffness, natural frequencies and mode shapes to determine the position and depth of the crack in the beam. Prasad et al. [1] investigated that the effect of crack position from free end to fixed end of the vibrating cantilever beam at each of the frequency on the resolve of crack growth rate. B. P. Nandwana and S. K. Maiti [2] have determined the crack position, crack depth and crack inclination by using finite element method and experimental method. Bing et al. [3] identified the multiple crack of beam by using a threestepmeshing method with less subdivision and more precision. It can be used to detection of multiple cracks of complicated structure. Sugumaran and Ramachandran [4] described the use of decision tree of a fuzzy classifier for choosing top few features that will distinguish the fault condition of the bearing from given trained samples. Law and Lu [5] have stated a time domain methods in which detect the crack parameters from strain or displacement measurements. Curadelli et al. [6] used wavelet transfer to identify structural damage by the help of Applied Mechanics and Materials Vols. 592-594 (2014) pp 1996-2000 Online available since 2014/Jul/15 at www.scientific.net © (2014) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMM.592-594.1996 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 59.145.203.66-16/07/14,07:44:50)