Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 385742, 17 pages
Research Article

Stability Analysis and Investigation of a Magnetoelastic Beam Subjected to Axial Compressive Load and Transverse Magnetic Field

1Department of Applied Mathematics, I-Shou University, Kaohsiung 840, Taiwan
2Department of Construction Engineering, National Kaohsiung First University of Science & Technology, Kaohsiung 824, Taiwan

Received 22 December 2009; Revised 22 April 2010; Accepted 3 June 2010

Academic Editor: Carlo Cattani

Copyright © 2010 Mei-Feng Liu and Tai-Ping Chang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The interactive behaviors between transverse magnetic fields and axial loads of a magnetoelastic (ME) beam subjected to general boundary conditions are investigated. In particular, the instability criterion for the magneto-mechanical buckling problem is intricately discussed based on the structure characteristics and the initial conditions. The equation of motion for the proposed physical model is introduced according to the Hamilton's principle, and the stability criterion is obtained by using the method of multiple scales implemented on both spatial and time domains. Eventually a so-called Schrodinger equation with cubic nonlinearity (NLS) can be generated by suitably changing the variables; as a result, the stable criterion for the magnetoelastic beam can be acquired after dissecting the nonlinear Schrodinger equation and requiring the imaginary part of the time domain solution to be vanished. Stability criterion curve for the dispersion equation of the ME beam is firstly depicted in order to reveal the magnificent influence of the structure characteristic itself, followed by the instability constraint due to the variation of initial conditions and the observation locations. The results indicate that the prior one actually denotes a parabola, whereas the latter one is sometimes a diamond-like or ellipse-like region spotting along the prior one.