Transient Response in a Bi-material Cylinder of Soft Ferromagnetic Material Subjected to Magnetic Shock
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ISSN 1860-2134
Transient Response in a Bi-material Cylinder of Soft Ferromagnetic Material Subjected to Magnetic Shock Zhangjianing Cheng1
Quan Jiang2
1
( College of Civil Engineering, Tongji University, Shanghai 200092, China) (2 School of Transportation and Civil Engineering, Nantong University, Nantong 226019, China)
Received 13 July 2020; revision received 21 October 2020; Accepted 26 October 2020 c The Chinese Society of Theoretical and Applied Mechanics 2020
ABSTRACT The transient response in a bi-material cylinder of soft ferromagnetic material under magnetic shock is investigated in this study. The analytical solutions for displacement and stress have been derived using the finite Hankel transform and the Laplace transform. The numerical examples show that the displacement and stress fields respond dynamically in the bi-material cylinder under magnetic shock. The derived displacement at the center and radial stress on the surface of the cylinder satisfy the boundary conditions, showing the correctness of calculation. The displacement and stress waves propagate from the surface to the center of the cylinder when the magnetic field is loaded. The stress fields increase from the center to the surface of the cylinder and are much larger than the quasi-static state since the waves reflect, collide and concentrate in the body of the cylinder. The method of this paper can be used in the design of soft ferromagnetic structures.
KEY WORDS Soft ferromagnetic material, Bi-material cylinder, Transient stress, Magnetic shock
1. Introduction The magnetic field intensity and magnetization vector are parallel in the rigid body of a soft ferromagnetic material, which can be widely used as the core structures for transformers, sensors, actuators and electric motors due to the magnetoelastic behavior. Eringen and Maugin [1] and Brown [2] gave the constitutive equations by considering the magnetoelastic coupling theory of soft magnetic materials, which, however, were difficult to be applied in engineering applications. Based on the assumption of low hysteresis and magnetization, Pao and Yeh [3] linearized Brown’s theory and gave the linear magnetoelastic constitutive equations of soft magnetic materials, which can be used in many problems. Zhao et al. [4] derived a theoretical framework to analyze magnetic materials and provided numerical examples for the design of complex shape-morphing structures. Kurlyandskaya et al. [5] analyzed the magnetic properties of soft magnetic materials in sensors at high frequency. Azuma et al. [6] studied the small core loss for a lower-rated amorphous wound core transformer with reduced thickness of soft magnetic ribbon. These studies have greatly promoted the theoretical and numerical research on soft ferromagnetic materials. The solutions of magnetoelastic problems are controlled by different constitutive equations and different types of boundary conditions [7], which can have different results. Shindo [8] studied the stress
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