NATURAL FREQUENCY OF STEPPED BEAM HAVING MULTIPLE OPEN CRACKS BY TRANSFER MATRIX METHOD

Chen, Q.; Fan, S.C.; Zheng, D.Y.

doi:10.1007/978-1-4020-3953-9_143

Q. Chen⁴,
S.C. Fan⁴ &
D.Y. Zheng⁴

1730 Accesses
2 Citations

Abstract

In this study, the transfer matrix method is used for the dynamic analysis of a stepped beam with arbitrary multiple transverse open cracks. The reduction in bending stiffness due to the presence of transverse open cracks or abrupt changes of cross-section is modelled by kind of massless rotational springs. The advantages are demonstrated through examples. Firstly, it yields purely analytical solutions which are more accurate than the numerical ones. Secondly, the size of the resulting eigen-matrix is small. For beams with all sorts of boundary restraint conditions, having many abrupt changes of cross-sections and/or with arbitrary multiple open cracks, the size of the eigen-matrix is still 4 by 4 (or less). Numerical examples are presented to validate the accuracy and efficiency of the present formulation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 259.00; Price excludes VAT (USA)

Softcover Book: USD 329.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

REFERENCES

A.D. Dimarogonas (1996), Vibration of cracked structures: a state of the art review. Enngineering Fracture Mechanics, 55, pp. 831–857.
Article Google Scholar
Q.S. Li (2001), Vibratory characteristics of multi-step beams with an arbitrary number of cracks and concentrated masses. Applied Acoustics, 62, pp. 691–706.
Article Google Scholar
N.T. Khiem and T.V. Lien (2001), A simplified method for natural frequency analysis of a multiple cracked beam. Journal of Sound and Vibration, 245, 4, pp. 737–751.
Article Google Scholar
T.G. Chondros, A.D. Dimarognas and J. Yao (1998), A continuous cracked beam vibration theory. Journal of Sound and Vibration, 215, pp. 17–34.
Article Google Scholar
D.Y. Zheng and N.J. Kessissoglou (2004), Free vibration analysis of a cracked beam by finite element method. Journal of Sound and Vibration, 273, pp. 457–475.
Article Google Scholar

Download references

Author information

Authors and Affiliations

School of Civil and Environmental Engineering, Nanyang Technological University, Nanyang Avenue, Singapore, 639798
Q. Chen, S.C. Fan & D.Y. Zheng

Authors

Q. Chen
View author publications
You can also search for this author in PubMed Google Scholar
S.C. Fan
View author publications
You can also search for this author in PubMed Google Scholar
D.Y. Zheng
View author publications
You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

National University of Singapore, Singapore
G.R. LIU
National University of Singapore, Singapore
V.B.C. TAN
Hunan University, P.R. China
X. HAN

Rights and permissions

Reprints and permissions

Copyright information

About this paper

Cite this paper

Chen, Q., Fan, S., Zheng, D. (2006). NATURAL FREQUENCY OF STEPPED BEAM HAVING MULTIPLE OPEN CRACKS BY TRANSFER MATRIX METHOD. In: LIU, G., TAN, V., HAN, X. (eds) Computational Methods. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-3953-9_143

Download citation

DOI: https://doi.org/10.1007/978-1-4020-3953-9_143
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3952-2
Online ISBN: 978-1-4020-3953-9
eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics