Nonlinear analysis and experiment for magnetoelastic buckling

磁致弹性屈曲非线性分析与实验

• 批准号: 06650275
• 负责人: AOSHIMA Nobuharu
• 金额: $ 1.34万
• 依托单位: University of Tsukuba
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1995
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-06650275/
• 关键词: Buckling; Magnetoelastic buckling; Nonlinear analysis; Bifurcation; Catastrophe; Stabilization control; クーロン摩擦; 機械力学; 分岐理論; 電磁構造連成

First, the catastrophe of the beam subjected to electromagnetic force is theoretically analyzed by taking into account the cubic nonlinearity of the electromagnetic and elastic forces with the deflection, and also of the unsymmetrical component of the current. Second, a method to stabilize the magnetoelastic buckling is theoretically proposed, and its validity is numerically confirmed. Third, the effect of Coulomb damping on the magnetoelastic buckling is theoretically and experimentally examined using a simple two rods system subjected to electromagnetic force. The main results are as follows :1. Using Liapunov-Schmidt method and center manifold theory, the bifurcation equation is obtained and the complement of the buckling mode is analyzed. For the case of neglecting the complement, the error of the solution is estimated, and it is shown that the third mode has a larger effect than the second mode on the mode shape of the postbuckling state.2. In the case when an unsymmetrical compon … More ent of the current is not present, a supercritical pitchfork bifurcation occurs due to the cubic nonlinear component of the elastic force associated with the stretching of the beam in the longitudinal direction. As a result, even in the postbuckling state, the deflection of the beam maintains a finite value. In the case when an unsymmetrical component of the current is present, it is shown theoretically that a cusp type catastrophe occurs.3. We present a method to stabilize the magnetoelastic buckling by controlling the perturbation of the bifurcation ; the condition of applicability of this method is governed by a relationship between the initial deflection of the beam and the switching time of control. The validity of the proposed control method is confirmed by numerical simulation, and also the effect of the delay of the switching is discussed.4. In the absence of Coulomb damping, there is generally one steady state in the case of prebuckling, but when Coulomb damping exists, there are infinite steady states. With approaching the magnetoelastic buckling point, the steady state region increases. Also for the case when the bifurcation is supercritical, Coulomb damping generates steady state region in the neighborhood of the nontrivial stable steady states which exist in the absence of Coulomb damping. On the other hand, for the case when the bifurcation is subcritical, the Coulomb damping generates steady state region in the neigh borhood of the nontrivial unstable steady states which exist in the absence of Coulomb damping. Less

首先，通过考虑到电磁和弹性力的立方非线性以及电流的不对称成分的电磁和弹性力的立方非线性，可以在理论上分析受到电磁力的光束的灾难。其次，从理论上提出了稳定磁屈曲的方法，其有效性基本上得到了证实。第三，在理论上和实验检查了库仑阻尼对磁屈曲的影响，并使用受到电磁力的简单两个杆系统进行了检查。主要结果如下：1。使用Liapunov-Schmidt方法和中心歧管理论，获得分叉方程，并分析了屈曲模式的完成。对于忽略完成的情况，估算了解决方案的误差，并且表明第三模式的效果大于第二模式在后扎后状态的模式上的效果。2。在不对称的组件……不存在更多电流的情况下，由于弹性力的立方非线性成分与纵向伸展的弹力相关的弹性力的立方非线性成分，发生了超临界的干草叉分叉。结果，即使在爆炸状态下，光束的定义也具有有限的值。在存在电流的不对称成分的情况下，理论上表明出现了尖齿型灾难。3。我们提出了一种通过控制分叉的扰动来稳定磁屈曲的方法。该方法的适用性条件受梁的初始定义与控制时间的转换时间之间的关系。提出的控制方法的有效性通过数值模拟证实，还讨论了切换延迟的效果。4。在没有库仑阻尼的情况下，通常存在一种稳态，但是当存在库仑阻尼时，存在无限的稳态。随着接近磁屈服点，稳态区域增加。同样，对于分叉是超临界的情况，库仑阻尼会在没有库仑阻尼的情况下存在于非平凡稳定稳态的邻居中。另一方面，对于分叉是亚临界的情况，库仑阻尼会在没有库仑阻尼的情况下在非平凡的不稳定稳态附近产生稳态区域。较少的

项目成果

Hiroshi YABUNO: "Buckling of a Beam Subjected to Electromagnetic Force and Its Stabilization by Controlling the perturbation of the Bifurcation" Nonlinear Dynamics. 9(印刷中). (1996)

Hiroshi YABUNO：“电磁力作用下梁的屈曲及其通过控制分叉扰动的稳定”非线性动力学 9（出版中）。

Hiroshi YABUNO: "Buckling of a Beam Subjected to Electromagnetic Force and Its Stabilization by Controlling the perturbation of the Bifurcation" Nonlinear Dynamics. 9(印刷中).

Hiroshi YABUNO：“电磁力作用下梁的屈曲及其通过控制分叉扰动实现稳定”非线性动力学 9（正在出版）。

H.YABUNO: "Buckling of a Beam subjected to electromagnetic Force and its Stabilization by controlling the Perturbation of the Bifurcation" Nonlinear Dynamics. Vol.9 (to appear.). (1996)

H.YABUNO：“电磁力作用下梁的屈曲及其通过控制分叉扰动实现稳定”非线性动力学。