Vibrations and stability analysis of double current-carrying strips interacting with magnetic field
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O R I G I NA L PA P E R
A. R. Hosseinian · R. D. Firouz-Abadi
Vibrations and stability analysis of double current-carrying strips interacting with magnetic field
Received: 21 March 2020 / Revised: 27 July 2020 / Accepted: 5 September 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract Interactive vibrations and buckling of double current-carrying strips (DCCS) are investigated in this study. Considering the rotational and transverse deformation of the strip, four coupled equations of motion are obtained using Hamilton’s principle. Using the Galerkin method, mass and stiffness matrices are extracted and the stability of the system is determined by solving the eigenvalue problem. Effects of pretension and elevated temperature on the stability of DCCS are studied for three types of materials and various arrangements. Finally, the effect of horizontal or vertical distance between strips on the critical current value is investigated. According to the results, the effects of temperature rise, pretension, and the relative distance of the strips on the instability of DCCS are found to be significant.
1 Introduction The dynamic behavior of conductive structures under the influence of a magnetic field has been studied extensively in the last half-century [1–7]. The force applied to the current-carrying wires in the presence of a magnetic field (known as the Lorentz force) can cause significant deformations in the wire depending on the intensity of the current and the magnetic field. Also, in certain situations, the wire may become unstable and buckle. In many areas of engineering, structural instability is considered to be an undesirable phenomenon, however, and in some circumstances, structural instability can be used as a smart tool in various types of sensors, actuators, electromechanical switches or many other industrial applications [8–11]. In this regard, many scientists have studied magneto-elastic problems and extracted the governing equations and tried to present engineering and practical models to identify this phenomenon. One of the earliest attempts in this field was the work of Dolbin and Morozov, who in 1966 investigated the bending vibrations of circular and elliptical electrically conducting wires under the influence of a magnetic field [12]. They were able to calculate the elastic instability boundary of the wires and obtain the corresponding electrical currents analytically. About 10 years later, Chattopadhyay and Moon [13] performed laboratory tests on current-carrying wires observing elastic instability. They compared the experimental results with theoretical calculations. In recent years, the magneto-elastic problem has been studied with two different approaches. The first approach is the nanoscaled magneto-elastic problem. Due to the wide industrial applications of the nanostructures, many studies are performed and numerous articles are published on the magneto-elastic field of nanostructures carrying electric current and the effects of a magnetic field on them [14–22]. In th
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