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1.
L. P. Zheleznov V. V. Kabanov D. V. Boiko 《Journal of Applied Mechanics and Technical Physics》2006,47(3):406-411
The stability problem of a cylindrical shell of oval cross section loaded by a bending moment and internal pressure is studied.
The variational displacement finite-element method is used. For the prebuckling stress-strain state, the bending and nonlinearity
are taken into account. The effects of the nonlinear nature of the deformation and the cross-sectional ovality of the shells
on the critical loads and buckling modes are determined.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 119–125, May–June, 2006. 相似文献
2.
Nonlinear interactions and chaotic dynamics of suspended cables with three-to-one internal resonances 总被引:2,自引:0,他引:2
Nonlinear planar oscillations of suspended cables subjected to external excitations with three-to-one internal resonances are investigated. At first, the Galerkin method is used to discretize the governing nonlinear integral–partial-differential equation. Then, the method of multiple scales is applied to obtain the modulation equations in the case of primary resonance. The equilibrium solutions, the periodic solutions and chaotic solutions of the modulation equations are also investigated. The Newton–Raphson method and the pseudo-arclength path-following algorithm are used to obtain the frequency/force–response curves. The supercritical Hopf bifurcations are found in these curves. Choosing these bifurcations as the initial points and applying the shooting method and the pseudo-arclength path-following algorithm, the periodic solution branches are obtained. At the same time, the Floquet theory is used to determine the stability of the periodic solutions. Numerical simulations are used to illustrate the cascades of period-doubling bifurcations leading to chaos. At last, the nonlinear responses of the two-degree-of-freedom model are investigated. 相似文献
3.
Principal parametric and three-to-one internal resonances of flexible beams undergoing a large linear motion 总被引:7,自引:0,他引:7
A set of nonlinear differential equations is established by using Kane‘s method for the planar oscillation of flexible beams undergoing a large linear motion. In the case of a simply supported slender beam under certain average acceleration of base, the second natural frequency of the beam may approximate the tripled first one so that the condition of 3 : 1 internal resonance of the beam holds true. The method of multiple scales is used to solve directly the nonlinear differential equations and to derive a set of nonlinear modulation equations for the principal parametric resonance of the first mode combined with 3 : 1 internal resonance between the first two modes. Then, the modulation equations are numerically solved to obtain the steady-state response and the stability condition of the beam. The abundant nonlinear dynamic behaviors, such as various types of local bifurcations and chaos that do not appear for linear models, can be observed in the case studies. For a Hopf bifurcation,the 4-dimensional modulation equations are reduced onto the central manifold and the type of Hopf bifurcation is determined. As usual, a limit cycle may undergo a series of period-doubling bifurcations and become a chaotic oscillation at last. 相似文献