Flexural Vibration and Elastic Buckling of a Cracked Timoshenko Beam Made of Functionally Graded Materials

By L. Ke, Junliang Yang, S. Kitipornchai, Yang Xiang. 2009

188 citations recorded by the source corpus.

Free vibration and elastic buckling of beams made of functionally graded materials (FGMs) containing open edge cracks are studied in this paper based on Timoshenko beam theory. The crack is modeled by a massless elastic rotational spring. It is assumed that the material properties follow exponential distributions along beam thickness direction. Analytical solutions of natural frequencies and critical buckling load are obtained for cracked FGM beams with clamped-free, hinged-hinged, and clamped-clamped end supports. A detailed parametric study is conducted to study the influences of crack depth, crack location, total number of cracks, material properties, beam slenderness ratio, and end supports on the free vibration and buckling characteristics of cracked FGM beams.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/8e9575489c9096c35481aed15cf5452757f5bde0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

1. S. Kitipornchai
2. Jie Yang
3. L. Ke
4. Mohammad Rafiee
5. A. Shooshtari
6. Junliang Yang
7. Shirong Li
8. Hui‐Shen Shen

In Mechanics of Materials

1. S. Kitipornchai
2. Jie Yang
3. Hui‐Shen Shen
4. Junliang Yang
5. Huu-Tai Thai
6. Ashraf M. Zenkour
7. L. Ke
8. Mohammad Rafiee

Citations in the corpus

• Thermal buckling analysis of functionally graded material beams (2010, background): “Khdeir (2001) studied the buckling of crossply laminated composite beams based on various beam theories and various edge conditions.”
• A higher-order theory for static and dynamic analyses of functionally graded beams (2010, background): “Recently, buckling, flexural vibration and postbuckling of cracked functionally graded Timoshenko beams have been studied in [16, 17 ].”
• An analytical study on the nonlinear vibration of functionally graded beams (2010, methodology): “Introducing the following dimensionless quantities [28, 29]”
• Dynamic Stability of Functionally Graded Carbon Nanotube-Reinforced Composite Beams (2013, background): “investigations on the static bending [21, 22], elastic buckling [23, 24], dynamic stability [24–29], postbuckling [30, 31], linear and nonlinear free vibration [32–37] of FGM beams, plates, and shells have been conducted for the past 20 years.”
• Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory (2013, unknown): “All rights reserved.”
• Nonlinear forced vibration analysis of clamped functionally graded beams (2011, methodology): “We introduce the following dimensionless quantities [ 26 ,27]:”
• Relations between buckling loads of functionally graded Timoshenko and homogeneous Euler-Bernoulli beams (2013, background): “[8,9] as well as Yang and Chen [10] studied free vibrations, buckling and post-buckling of FGM TBs containing open cracks by assuming an exponential variation of material properties in the thickness direction.”