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Free vibration analysis of a single edge cracked symmetric functionally graded stepped beams

Free vibration analysis of a single edge cracked symmetric functionally graded stepped beams Free vibration analysis of a single edge cracked multi-layered symmetric sandwich stepped Timoshenko beams, made of functionally graded materials, is studied using finite element method and linear elastic fracture mechanic theory. The cantilever functionally graded beam consists of 50 layers, assumed that the second stage of the beam (step part) is created by machining. Thus, providing the material continuity between the two beam stages. It is assumed that material properties vary continuously, along the thickness direction according to the exponential and power laws. A developed MATLAB code is used to find the natural frequencies of three types of the stepped beam, concluding a good agreement with the known data from the literature, supported also by ANSYS software in data verification. In the study, the effects of the crack location, crack depth, power law gradient index, different material distributions, different stepped length, different cross-sectional geometries on natural frequencies and mode shapes are analysed in detail. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Structural Engineering SAGE

Free vibration analysis of a single edge cracked symmetric functionally graded stepped beams

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Publisher
SAGE
Copyright
© The Author(s) 2020
ISSN
1369-4332
eISSN
2048-4011
DOI
10.1177/1369433220939214
Publisher site
See Article on Publisher Site

Abstract

Free vibration analysis of a single edge cracked multi-layered symmetric sandwich stepped Timoshenko beams, made of functionally graded materials, is studied using finite element method and linear elastic fracture mechanic theory. The cantilever functionally graded beam consists of 50 layers, assumed that the second stage of the beam (step part) is created by machining. Thus, providing the material continuity between the two beam stages. It is assumed that material properties vary continuously, along the thickness direction according to the exponential and power laws. A developed MATLAB code is used to find the natural frequencies of three types of the stepped beam, concluding a good agreement with the known data from the literature, supported also by ANSYS software in data verification. In the study, the effects of the crack location, crack depth, power law gradient index, different material distributions, different stepped length, different cross-sectional geometries on natural frequencies and mode shapes are analysed in detail.

Journal

Advances in Structural EngineeringSAGE

Published: Dec 1, 2020

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