Dynamics of a Cracked Cantilever Beam Subjected to a Moving Point Force Using Discrete Element Method
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ORIGINAL PAPER
Dynamics of a Cracked Cantilever Beam Subjected to a Moving Point Force Using Discrete Element Method Anand Kumar Agrawal1 · Goutam Chakraborty1 Received: 23 June 2020 / Revised: 9 October 2020 / Accepted: 3 November 2020 © Krishtel eMaging Solutions Private Limited 2020
Abstract Purpose This work aims to investigate a cracked cantilever beam subjected to a moving point force using the Discrete Element Method (DEM). Contribution and Method A novel approach to mathematically include a moving force in discrete element formulation of a cracked beam is the main contribution of this paper. The local reduction in the stiffness of the cantilever beam due to the presence of a crack has been accounted for by a popularly used result from fracture mechanics. Hence, the present work provides an alternative approach to numerically evaluate the forced vibration of cracked beams under the application of a moving point force. Conclusion The methodology has been verified by comparing some of the results obtained here to those obtained using an already published analytical method. In the end, the effects of crack length, crack location, and force-velocity on the dynamic behavior of the cracked beam are studied using the proposed methodology. The proposed method can provide an effective alternative for the analysis of cracked beams subjected to a moving point force. Keywords Discrete element method (DEM) · Beam with a moving point force · Cracked beam · Moving load
Introduction Detection, localization, and quantification of cracks in structures are basic objectives of SHM. Usually, these objectives are achieved by analyzing the signals obtained from various sensors using modern signal processing techniques [1, 2]. Therefore, it is beneficial to know how these signals are expected to look in various structural conditions, which makes it important to investigate the behavior of damaged structures. Experimental investigations to characterize the presence of a crack in a beam carried out by Chatterjee and Vaidya [3] substantiate the importance of such studies. Moreover, in the case of model-based structural health monitoring, mathematical models are updated using the sensor data to achieve damage identification in structures [4]. Various experimental, theoretical, and numerical studies have been conducted to investigate the behavior of these * Anand Kumar Agrawal [email protected] 1
Systems, Dynamics and Control Laboratory, Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur 721302, W.B., India
structures. Beams are one of the most studied structural members because many structural, as well as machine components, can be modeled as beams. Modeling of cracked beams has been done by various methods and cracked beams under many different loadings and boundary conditions have been studied [5–7]. One class of method is to model the cracked beam as two parts joined by a rotational spring whose stiffness is related to the crack depth as in [8, 9]. For example, Narkis [10] modeled
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