Parametric instability of functionally graded Timoshenko beams with an open edge crack

Jie Yang; Sritawat Kitipornchai; Yang Xiang

Parametric instability of functionally graded Timoshenko beams with an open edge crack

Jie Yang
, Sritawat Kitipornchai
, Yang Xiang

School of Engineering, Design & Built Environment

Research output: Chapter in Book / Conference Paper › Conference Paper

Abstract

This paper studies the parametric instability of functionally graded beams with open edge cracks subjected to an axial excitation. The beam is clamped at both ends and movable in the longitudinal direction with materials properties varying exponentially through the thickness direction. Theoretical formulations are based on Timoshenko beam theory and the linear rotational spring model. The governing equations of motion are derived by using the Hamilton's principle and solved by using Galerkin's technique and the Least Squares method. The boundary points on the unstable regions are determined by Bolotin's method. Numerical results are presented to show the influences of crack location, crack depth, material property gradient, and beam slenderness ratio on the principal unstable region of the cracked functionally graded beams.

Original language	English
Title of host publication	ISCM II and EPMESC XII : Proceedings of the 2nd International Symposium on Computational Mechanics and the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science, Hong Kong-Macau, China, 30 November-3 December 2009
Publisher	American Institute of Physics
Pages	107-112
Number of pages	6
ISBN (Print)	9780735407787
Publication status	Published - 2009
Event	International Symposium on Computational Mechanics (ISCM II) in conjunction with the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science (EPMESC XII) - Duration: 1 Jan 2009 → …

Conference

Conference	International Symposium on Computational Mechanics (ISCM II) in conjunction with the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science (EPMESC XII)
Period	1/01/09 → …

Keywords

beams
Timoshenko beam theory

Cite this

Yang, J., Kitipornchai, S., & Xiang, Y. (2009). Parametric instability of functionally graded Timoshenko beams with an open edge crack. In ISCM II and EPMESC XII : Proceedings of the 2nd International Symposium on Computational Mechanics and the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science, Hong Kong-Macau, China, 30 November-3 December 2009 (pp. 107-112). American Institute of Physics.

Yang, Jie ; Kitipornchai, Sritawat ; Xiang, Yang. / Parametric instability of functionally graded Timoshenko beams with an open edge crack. ISCM II and EPMESC XII : Proceedings of the 2nd International Symposium on Computational Mechanics and the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science, Hong Kong-Macau, China, 30 November-3 December 2009. American Institute of Physics, 2009. pp. 107-112

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title = "Parametric instability of functionally graded Timoshenko beams with an open edge crack",

abstract = "This paper studies the parametric instability of functionally graded beams with open edge cracks subjected to an axial excitation. The beam is clamped at both ends and movable in the longitudinal direction with materials properties varying exponentially through the thickness direction. Theoretical formulations are based on Timoshenko beam theory and the linear rotational spring model. The governing equations of motion are derived by using the Hamilton's principle and solved by using Galerkin's technique and the Least Squares method. The boundary points on the unstable regions are determined by Bolotin's method. Numerical results are presented to show the influences of crack location, crack depth, material property gradient, and beam slenderness ratio on the principal unstable region of the cracked functionally graded beams.",

keywords = "beams, Timoshenko beam theory",

author = "Jie Yang and Sritawat Kitipornchai and Yang Xiang",

year = "2009",

language = "English",

isbn = "9780735407787",

pages = "107--112",

booktitle = "ISCM II and EPMESC XII : Proceedings of the 2nd International Symposium on Computational Mechanics and the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science, Hong Kong-Macau, China, 30 November-3 December 2009",

publisher = "American Institute of Physics",

address = "United States",

note = "International Symposium on Computational Mechanics (ISCM II) in conjunction with the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science (EPMESC XII) ; Conference date: 01-01-2009",

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Yang, J, Kitipornchai, S & Xiang, Y 2009, Parametric instability of functionally graded Timoshenko beams with an open edge crack. in ISCM II and EPMESC XII : Proceedings of the 2nd International Symposium on Computational Mechanics and the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science, Hong Kong-Macau, China, 30 November-3 December 2009. American Institute of Physics, pp. 107-112, International Symposium on Computational Mechanics (ISCM II) in conjunction with the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science (EPMESC XII), 1/01/09.

Parametric instability of functionally graded Timoshenko beams with an open edge crack. / Yang, Jie; Kitipornchai, Sritawat; Xiang, Yang.
ISCM II and EPMESC XII : Proceedings of the 2nd International Symposium on Computational Mechanics and the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science, Hong Kong-Macau, China, 30 November-3 December 2009. American Institute of Physics, 2009. p. 107-112.

Research output: Chapter in Book / Conference Paper › Conference Paper

TY - GEN

T1 - Parametric instability of functionally graded Timoshenko beams with an open edge crack

AU - Yang, Jie

AU - Kitipornchai, Sritawat

AU - Xiang, Yang

PY - 2009

Y1 - 2009

N2 - This paper studies the parametric instability of functionally graded beams with open edge cracks subjected to an axial excitation. The beam is clamped at both ends and movable in the longitudinal direction with materials properties varying exponentially through the thickness direction. Theoretical formulations are based on Timoshenko beam theory and the linear rotational spring model. The governing equations of motion are derived by using the Hamilton's principle and solved by using Galerkin's technique and the Least Squares method. The boundary points on the unstable regions are determined by Bolotin's method. Numerical results are presented to show the influences of crack location, crack depth, material property gradient, and beam slenderness ratio on the principal unstable region of the cracked functionally graded beams.

AB - This paper studies the parametric instability of functionally graded beams with open edge cracks subjected to an axial excitation. The beam is clamped at both ends and movable in the longitudinal direction with materials properties varying exponentially through the thickness direction. Theoretical formulations are based on Timoshenko beam theory and the linear rotational spring model. The governing equations of motion are derived by using the Hamilton's principle and solved by using Galerkin's technique and the Least Squares method. The boundary points on the unstable regions are determined by Bolotin's method. Numerical results are presented to show the influences of crack location, crack depth, material property gradient, and beam slenderness ratio on the principal unstable region of the cracked functionally graded beams.

KW - beams

KW - Timoshenko beam theory

UR - http://handle.uws.edu.au:8081/1959.7/504409

M3 - Conference Paper

SN - 9780735407787

SP - 107

EP - 112

BT - ISCM II and EPMESC XII : Proceedings of the 2nd International Symposium on Computational Mechanics and the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science, Hong Kong-Macau, China, 30 November-3 December 2009

PB - American Institute of Physics

T2 - International Symposium on Computational Mechanics (ISCM II) in conjunction with the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science (EPMESC XII)

Y2 - 1 January 2009

ER -

Yang J, Kitipornchai S, Xiang Y. Parametric instability of functionally graded Timoshenko beams with an open edge crack. In ISCM II and EPMESC XII : Proceedings of the 2nd International Symposium on Computational Mechanics and the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science, Hong Kong-Macau, China, 30 November-3 December 2009. American Institute of Physics. 2009. p. 107-112

Parametric instability of functionally graded Timoshenko beams with an open edge crack

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