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71.
In this paper, the wind-induced, horizontal vibrations of a vertical Euler–Bernoulli beam will be considered. At the top of
the beam, a tuned mass damper (TMD) has been installed. The horizontal vibrations can be described by an initial-boundary
value problem. Perturbation methods will be applied to construct approximations of the solutions of the initial-boundary value
problem, and it will be shown that the TMD uniformly damps the oscillation modes of the beam. In the analysis, it will be
assumed that damping, wind-force, and gravity effects are small but not negligible. 相似文献
72.
Hou Weijian Yu Tongxi Su Xianyue Department of Mechanics Peking University Beijing P. R. China Department of Mechanical Engineering UMIST Manchester M QD UK 《Acta Mechanica Solida Sinica》1995,8(1):32-44
A lumped masses-springs model is proposed to analyze the dynamicresponse of an elastic-plastic cantilever beam resulting from impact. The numericalresults are in good agreement with those by finite-element approaches. The simplifiedmodel can catch the most essential features of elastic-plastic response of beams; inparticular, it demonstrates the effect of elastic deformation on the distribution ofbending moment and energy dissipation, and provides valuable quatitative results. 相似文献
73.
In this paper the nonlinear response of a base-excited slender beam carrying an attached mass is investigated with 1:3:9 internal resonances for principal and combinationparametric resonances. Here the method of normal forms is used to reduce the second order nonlinear temporal differential equation of motion of the system to a set offirst order nonlinear differential equations which are used to find the fixed-point, periodic, quasi-periodic and chaotic responses of the system.Stability and bifurcation analysis of the responses are carried out and bifurcation sets are plotted. Many chaotic phenomena are reported in this paper. 相似文献
74.
75.
76.
非惯性系下柔性悬臂梁的振动主动控制 总被引:4,自引:2,他引:4
采用变结构控制方法对非惯性系下柔性悬臂梁的振动主动控制进行研究.重点通过算例揭示一次近似模型与传统的零次近似模型的巨大差异,以及变结构方法在控制非惯性系下柔性悬臂梁的稳态振动的有效性.结果表明,当大范围旋转运动角速度较大时,传统零次近似模型不能对动力系统进行正确的数学描述;变结构控制方法能够使得非惯性系下梁的稳态振动得到完全镇定,且该方法对转动角速度变化具有较好的鲁棒性;采用零次近似模型进行控制设计的控制效果将在某一临界角速度条件下出现失效,该临界角速度值大于静止悬臂梁的基频. 相似文献
77.
78.
79.
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
80.
On the Discretization of Distributed-Parameter Systems with Quadratic and Cubic Nonlinearities 总被引:2,自引:0,他引:2
Approximate methods for analyzing the vibrations of an Euler--Bernoulli beam resting on a nonlinear elastic foundation are discussed. The cases of primary resonance (
n
) and subharmonic resonance of order one-half ( 2
n
), where is the excitation frequency and
n
is the natural frequency of the nth mode of the beam, are investigated. Approximate solutions based on discretization via the Galerkin method are contrasted with direct application of the method of multiple scales to the governing partial-differential equation and boundary conditions. The amplitude and phase modulation equations show that single-mode discretization leads to erroneous qualitative as well as quantitative predictions. Regions of softening (hardening) behavior of the system, the spatial dependence of the response drift, and frequency-response curves are numerically evaluated and compared using both approaches. 相似文献