Structural Engineering and Mechanics

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A transfer matrix method for in-plane bending vibrations of tapered beams with axial force and multiple edge cracks

  • Lee, Jung Woo (Department of Mechanical System Engineering, Kyonggi University) ;
  • Lee, Jung Youn (Department of Mechanical System Engineering, Kyonggi University)
  • Received : 2017.07.04
  • Accepted : 2018.02.27
  • Published : 2018.04.10
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Abstract

This paper proposes a transfer matrix method for the bending vibration of two types of tapered beams subjected to axial force, and it is applied to analyze tapered beams with an edge or multiple edge open cracks. One beam type is assumed to be reduced linearly in the cross-section height along the beam length. The other type is a tapered beam in which the cross-section height and width with the same taper ratio is linearly reduced simultaneously. Each crack is modeled as two sub-elements connected by a rotational spring, and the method can evaluate the effect of cracking on the desired number of eigenfrequencies using a minimum number of subdivisions. Among the power series available for the solutions, the roots of the differential equation are computed using the Frobenius method. The computed results confirm the accuracy of the method and are compared with previously reported results. The effectiveness of the proposed methods is demonstrated by examining specific examples, and the effects of cracking and axial loading are carefully examined by a comparison of the single and double tapered beam results.

Keywords

Acknowledgement

Supported by : Kyonggi University

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