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，考虑电磁力和弹力与偏转的三次非线性以及电流的不对称分量，对电磁力作用下的梁的突变进行理论分析。其次，提出一种稳定磁致弹性屈曲的方法。第三，库仑阻尼对磁致弹性屈曲的影响通过简单的两杆系统进行了理论和实验检验。主要结果如下： 1．利用Liapunov-Schmidt方法和中心流形理论，得到了屈曲模态的分岔方程，并分析了忽略补数情况下的解的误差。估计，结果表明，第三模态对屈曲后模态形状的影响比第二模态更大。2．在不存在电流不对称分量的情况下，a．超临界干草叉分岔是由于与梁纵向拉伸相关的弹力的三次非线性分量而发生的，因此，即使在后屈曲状态下，梁的挠度也保持有限值。电流的不对称分量存在，理论上表明会发生尖点型突变。 3．我们提出了一种通过控制分岔条件来稳定磁弹性屈曲的方法。该方法的适用性取决于梁的初始偏转与控制切换时间之间的关系，通过数值模拟验证了该控制方法的有效性，并讨论了切换延迟的影响。4。在没有库仑阻尼的情况下，预屈曲的情况下通常存在一个稳态，但是当库仑阻尼存在时，存在无限个稳态，随着接近磁弹性屈曲点，稳态区域也会增加。分岔是超临界的，库仑阻尼在没有库仑阻尼的情况下存在的非平凡稳定稳态附近产生稳态区域。另一方面，对于分岔是亚临界的情况，库仑阻尼在非平凡稳定稳态附近产生稳态区域。在没有库仑阻尼的情况下存在的非平凡不稳定稳态的邻域。

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。