Nonlinear analysis and experiment for magnetoelastic buckling
Project/Area Number  06650275 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
Dynamics/Control

Research Institution  University of Tsukuba 
Principal Investigator 
AOSHIMA Nobuharu Univ.of Tsukuba, Institute of Applied physics.Prof., 物理工学系, 教授 (60013710)

CoInvestigator(Kenkyūbuntansha) 
YABUNO Hiroshi Univ.of Tsukuba, Institute of Applied physics.Asst.Prof., 物理工学系, 講師 (60241791)

Project Fiscal Year 
1994 – 1995

Project Status 
Completed(Fiscal Year 1995)

Budget Amount *help 
¥2,100,000 (Direct Cost : ¥2,100,000)
Fiscal Year 1995 : ¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1994 : ¥1,200,000 (Direct Cost : ¥1,200,000)

Keywords  Buckling / Magnetoelastic buckling / Nonlinear analysis / Bifurcation / Catastrophe / Stabilization control / 座屈 / 電磁弾性座屈 / 非線形解析 / 分岐 / カタストロフィー / 安定化制御 / クーロン摩擦 / 機械力学 / 分岐理論 / 電磁構造連成 
Research Abstract 
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 LiapunovSchmidt 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
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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

Report
(4results)
Research Output
(4results)