1995 Fiscal Year Final Research Report Summary
Nonlinear analysis and experiment for magnetoelastic buckling
| Project/Area Number |
06650275
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
Dynamics/Control
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| Research Institution | University of Tsukuba |
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Principal Investigator |
AOSHIMA Nobuharu Univ.of Tsukuba, Institute of Applied physics.Prof., 物理工学系, 教授 (60013710)
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| Co-Investigator(Kenkyū-buntansha) |
YABUNO Hiroshi Univ.of Tsukuba, Institute of Applied physics.Asst.Prof., 物理工学系, 講師 (60241791)
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| Project Period (FY) |
1994 – 1995
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| Keywords | Buckling / Magnetoelastic buckling / Nonlinear analysis / Bifurcation / Catastrophe / Stabilization control / クーロン摩擦 |
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| 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 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
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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
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