Influence of Crack Inclination Angle on Isotropic Cracked Cantilever Beam
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Influence of Crack Inclination Angle on Isotropic Cracked Cantilever Beam Ehab Samir Mohamed Mohamed Soliman
Submitted: 24 June 2020 ASM International 2020
Abstract The influence of various crack inclination angles on the mode shape, rotational stiffness at the cracked cross section and the stiffness of the cracked cantilever beam was investigated. Finite element analysis for different scenarios of inclined cracked cantilever beam has been performed to obtain frequencies and zero frequency deflections. Rotational spring is considered as a simulation of the cracked section and based on zero frequency deflection; rotational spring stiffness and stiffness of cracked beam are analytically calculated. Also, the first three mode shapes of bending vibration and harmonic response are extracted and studied. The investigation of results revealed that the effect of inclined crack with / = 40, / = 55 and / = 120, respectively, is much, moderate and minimum severe, respectively, on the cracked cantilever beam. Keywords Mode shape Cantilever beam Rotational spring stiffness Harmonic response Inclined crack
Introduction In mechanical structures, monitoring and identification of crack damage is an important interest where catastrophic failures can be caused by the propagation of incipient cracks [1]. The dynamic characteristics and the safety of machineries are subjected to great influences by cracks due to fatigue and early crack detection, and diagnosis is an E. S. M. M. Soliman (&) Mechatronics and Robotics Department, Faculty of Engineering, Egyptian Russian University, Badr City, Cairo 11829, Egypt e-mail: [email protected]
important task for industrial maintenance to prevent catastrophic failure of machineries [2]. In machine members, operational problems and premature failure have been observed due to the presence of cracks [3]. The crack present in an elastic beam element causes the local flexibility due to the strain energy concentration in the vicinity of the crack tip under load [4]. The crack parameters of the beam, i.e., crack location and crack depth, can be determined by collected vibration data from a single point on the defective component [5]. The change in mode shapes, natural frequency, stiffness and damping ratio are affected by the presence of cracks in structure, and the vibrationbased nondestructive technique (NDT) works upon the measured mode shapes and frequency [6]. Many researchers studied the vibration behavior of the cracked cantilever beam and obtained natural frequencies of mode shapes of bending vibration [7–12]. Free vibration of a cracked beam has been studied by most of researchers under classical boundary conditions such as clamped– clamped, free–free, clamped-free and simply supported [13]. Bhaurkar and Thakur [14] obtained natural frequencies for single cracked cantilever beams for constant crack location but varying depth using modal analysis in ANSYS software. They determined frequencies of uncracked beam using ANSYS and calculated frequency ratio as the f
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