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Nonlinear analysis and experiment for magnetoelastic buckling

磁致弹性屈曲非线性分析与实验

基本信息

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

项目摘要

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，通过考虑电磁力和弹性力与挠度的立方非线性以及电流的非对称分量，从理论上分析了梁在电磁力作用下的突变。其次，从理论上提出了稳定磁弹性屈曲的方法，并从数值上验证了该方法的有效性。第三，利用一个简单的受电磁力作用的双杆系统，从理论和实验上研究了库仑阻尼对磁弹性屈曲的影响。主要结果如下：1.利用Liapunov-Schmidt方法和中心流形理论，得到了系统的分叉方程，并分析了屈曲模式的补充性。在忽略余项的情况下，对解的误差进行了估计，结果表明，第三模比第二模对后屈曲状态的振型有更大的影响。在不对称元件…的情况下在不存在更大电流的情况下，由于与梁的纵向拉伸相关的弹性力的立方非线性分量，出现了超临界干叉分叉。因此，即使在后屈曲状态，梁的挠度也保持有限的值。在电流不对称分量存在的情况下，从理论上证明了尖点突变的发生。我们提出了一种通过控制分叉的摄动来稳定磁弹性屈曲的方法，该方法的适用条件取决于梁的初始挠度与控制切换时间之间的关系。通过数值仿真验证了该控制方法的有效性，并讨论了切换延迟对控制效果的影响。在没有库仑阻尼力的情况下，预屈曲情况下一般只有一个稳态，但当有库仑阻尼力时，有无限个稳态。随着接近磁弹性屈曲点，稳态区增大。另外，对于超临界分叉的情况，库仑阻尼器在没有库仑阻尼器的情况下存在的非平凡稳态的邻域内产生稳态区。另一方面，对于亚临界分叉的情况，库仑阻尼在非平凡不稳定定态的附近产生了定态区，这些非平凡的不稳定定态在没有库仑阻尼的情况下存在。较少