International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 02 Issue: 09 | Dec-2015 www.irjet.net p-ISSN: 2395-0072 © 2015, IRJET ISO 9001:2008 Certified Journal Page 259 VIBRATION ANALYSIS OF SIMPLY SUPPORTED BEAM WITH ǮVǯ NOTCH CRACK A.I. Deokar 1 , S.D. Katekar 2 SKN Sinhgad college of Engineering Pandharpur, Maharashtra, India ---------------------------------------------------------------------***---------------------------------------------------------------------- Abstract - Dynamic behavior of simply supported cracked beam subjected to loading condition is analyzed in this paper. A systematic approach has been adopted in the present investigation by FEA Software ANSYS 11 for evaluation of natural frequencies and mode shapes. A simple elastic simply supported beam with crack at the different locations and also having different crack depth is considered for the modal analysis. It is found that the frequency of beam when the crack is in the middle position is less than the frequency with crack near the end position and the natural frequency of beam decreasing with increasing of crack depth due to decreasing of beam stiffness at any location of crack in beam. The beam is of mild steel material having properties as Young’s modulus ȋEȌ= ͸ͷͶ GPA, Poisson’s ratio= Ͷ.͸;, density= ͽ;ͼͶkg/mm 3 Keywords— Crack, crack depth, crack location, loading condition. 1. Introduction A structure is subjected to different types of loadings such as tension, bending, torsion or combined loads of tension and torsion or bending and torsion. Region where stress increase known as local stress concentrations, in this regions cracks are developed with an extremely high magnitude of stresses. Under repeated loading, cracks may develop at the surface and grow across the section. The presences of crack not only cause a local variation in the stiffness but it also affects the mechanical behavior of the entire structure to a considerable extent. A crack or local defect affects the vibration response of structural member. It results in changes of natural frequencies and mode shapes. Also crack may be classified on the basis of geometry and orientation as cracks parallel to shaft axis are known as longitudinal cracks, cracks that are open and close when affected part of material is subjected to alternative stresses are known as breathing crack, crack which are perpendicular to the axis of shaft are known as transverse crack, cracks on surface which are not visible known as sub- surface crack, crack which appear on the surface are known as surface crack. Surface cracks either circumferential or semi elliptical shape. Modal analysis is a worldwide used methodology that allows fast and reliable identification of system dynamics in complex structures. In the last decades several methods have been developed in quest to improve accuracy of modal models extracted from test data and to enlarge the applicability of modal analysis in industrial context. Structures vibrate in special shapes called mode shapes when excited at their resonant frequencies. A mode shape is the characteristics deformation shape defined by relative amplitudes of the extreme positions of vibration of a system at a single natural frequency. The research work in two decades has been published on the detection and diagnosis of crack developed by using vibration and acoustic methods. The literature survey of some papers given below: Hai-Ping Lin [2] has studied an analytical transfer matrix method, is used to solve the direct and inverse problems of simply supported beams with an open crack. The crack is modeled as a rotational spring with sectional flexibility. The natural frequencies of a cracked system can easily be obtained through many of the structural testing methods. When any two natural frequencies of a cracked simply supported beam are obtained from measurements, the location and the sectional flexibility of the crack can then be determined from the identification equation and the characteristic equation. Shuncong Zhong et.al.[4] has studied Natural frequencies of a damaged simply supported beam with a stationary roving mass. The transverse deflection of the cracked beam is constructed by adding a polynomial function, which represents the effects of a crack, to the polynomial function which represents the response of the intact beam. Kevin D. Murphy et.al. [5] has investigated vibration and stability characteristics of a cracked beam translating between fixed supports Using Hamilton's principle and elementary fracture mechanics, the equations of motion for the beam are developed. Throughout this