Investigation of Crack Effects on Isotropic Cantilever Beam
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TECHNICAL ARTICLE—PEER-REVIEWED
Investigation of Crack Effects on Isotropic Cantilever Beam Ehab Samir Mohamed Mohamed Soliman
Submitted: 4 March 2019 / in revised form: 20 July 2019 Ó ASM International 2019
Abstract The effect of an open edge crack on the parameters of an isotropic aluminum cantilever beam was investigated. The rotational stiffness and flexibility of the cantilever beam crack were analytically calculated for various crack depths. The results showed that as the depth of the crack increased, the rotational stiffness decreased and flexibility increased. For the intact cantilever beam, acceptable variation was validated by comparing the analytically estimated natural frequencies of the first three modes of bending vibration, and those obtained through modal analysis using the block Lanczos method of finite element analysis software ANSYS v16. The software was used to perform a structural, modal and harmonic analysis of the cracked cantilever beam under different scenarios. The results showed a reduction in the natural frequencies with the existence of the crack. The amount of the reduction varied based on the location and depth of the crack and the pattern of mode shapes. The calculated value of stiffness of the cantilever beam decreased with the presence of the crack. The amount of the decrease was dependent on the depth and location of the crack. The calculated values of the (SIF) stress intensity factor in mode I of the crack (opening edge crack) were proportional to the depth of the crack and inversely proportional to the distance of the crack from the fixed end of the cantilever beam. Based on these results, it is inferred that changes in the modal and structural parameters of the cracked cantilever beam were evidence which could be used to identify cracks.
E. S. M. M. Soliman (&) Mechatronics and Robotics Department, Faculty of Engineering, Egyptian Russian University, Badr City, Cairo 11829, Egypt e-mail: [email protected]
Keywords Rotational stiffness Modal analysis Harmonic analysis Cracked cantilever beam FEA
Introduction Cracks initiated by fatigue are a major problem in the dynamic structure of industrial machinery where they can cause accidents and failures [1]. The vibration behavior of beams changes when cracks occur, so action can be taken to prevent more damage [2]. Natural frequencies and mode shapes can be used to distinguish between healthy and unhealthy structures [3]. Cantilever beams are used in many mechanical structures, and researchers have studied cracked cantilever beams [4–6]. Choudhury et al. [3] carried out a theoretical analysis of a cracked cantilever beam and observed that frequency values change along with crack depth and crack location. They observed changes in frequency behavior in the first three modes of vibrations. Their results indicated that the range of natural frequency increased for different crack locations and depths at higher modes of vibration. They outlined a new optimization method for estimation of results based on location and depth o
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