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周雪, 王琳, 陈伟, 杨文正, 郭梓龙. 梯度磁场下变截面硬磁软梁的大变形力学行为. 力学学报, 2023, 55(8): 1699-1710. DOI: 10.6052/0459-1879-23-138
引用本文: 周雪, 王琳, 陈伟, 杨文正, 郭梓龙. 梯度磁场下变截面硬磁软梁的大变形力学行为. 力学学报, 2023, 55(8): 1699-1710. DOI: 10.6052/0459-1879-23-138
Zhou Xue, Wang Lin, Chen Wei, Yang Wenzheng, Guo Zilong. Large deformation of hard magnetic soft beam with variable cross section under gradient magnetic field. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(8): 1699-1710. DOI: 10.6052/0459-1879-23-138
Citation: Zhou Xue, Wang Lin, Chen Wei, Yang Wenzheng, Guo Zilong. Large deformation of hard magnetic soft beam with variable cross section under gradient magnetic field. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(8): 1699-1710. DOI: 10.6052/0459-1879-23-138

梯度磁场下变截面硬磁软梁的大变形力学行为

LARGE DEFORMATION OF HARD MAGNETIC SOFT BEAM WITH VARIABLE CROSS SECTION UNDER GRADIENT MAGNETIC FIELD

  • 摘要: 文章研究变截面参数和梯度磁场作用对硬磁软梁的大变形的影响, 为研制先进的硬磁软材料器件和系统提供理论指导. 基于最小势能原理, 建立了梯度磁场作用下变截面硬磁软梁静变形的力学理论模型. 基于线性稳定性理论, 分析了变截面对硬磁软梁屈曲失稳行为的影响. 基于非线性力学理论, 研究了变截面参数对硬磁软梁的后屈曲构型和弯曲变形的影响. 在此基础上, 深入研究了磁场梯度对变截面硬磁软梁大变形力学行为的影响. 研究结果表明, 变截面参数对硬磁软梁的临界屈曲载荷有较大影响, 通过改变变截面参数值可调节梁的屈曲稳定性. 当弯曲变形较小时, 变截面参数对硬磁软梁后屈曲构型和横向变形的影响不可忽略, 而这种影响在弯曲变形趋于饱和时, 则变得很弱. 磁场梯度参数的增大可引起变截面硬磁软梁出现更大幅值的静变形. 当磁场梯度参数增大而使磁场力大于屈曲临界载荷时, 变截面硬磁软梁不会出现前屈曲变形, 而直接导致梁发生非线性的后屈曲变形. 研究结果还显示, 增大磁场梯度参数可以提高变截面硬磁软梁自由端的磁偏转精度, 从而可有效地控制变截面硬磁软梁的磁转向. 研究结果可为基于硬磁软材料的可展开柔性结构、柔性电子器件和软体机器人等结构设计提供指导.

     

    Abstract: This paper reveals the effects of the variable cross section and the gradient magnetic field on the large deformations of hard magnetic soft (HMS) beams, which may provide theoretical guidance for the development of advanced magnetoactive devices and systems. Based on the principle of minimum potential energy, a theoretical model is established to calculate the static deformation of the HMS beam with a variable cross section under the gradient magnetic field. The effect of the variable cross section on the buckling instability behavior of the HMS beam is analyzed by using a linear stability theory. The nonlinear analysis method is employed to study the effects of the variable cross section and the magnetic field gradient on bending deformations of the HMS beam. It is found that the variable section parameter plays a significant role on the critical buckling load of the HMS beam, i.e. the buckling stability of the beam can be well tuned by changing the variable section parameter. When the bending deformation is relatively small, the effect of the variable section parameter on the post-buckling configuration of the HMS beam is obvious. Such effect becomes weak when the beam’s bending deformation tends to saturation. The increase of the magnetic field gradient parameter will lead to a larger static deformation of the HMS beam with a variable section. When the magnetic field force exceeds the critical buckling load, the variable-section HMS beam will not suffer the pre-buckling deformation, but directly translates to a nonlinear post-buckling deformation. The results also show that the accuracy of the magnetic deflection at the free end of the variable-section HMS beam can be improved by increasing the parameter value of the magnetic field gradient, which can increase the control effectiveness of the magnetic steering of the HMS beam with a variable section. This work may be useful for the design of deployable flexible structures, flexible electronic devices and soft robots based on HMS materials.

     

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