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11.
The paper addresses the forced flexural-and-torsional vibrations of a cantilever beam of constant cross section. The relevant
boundary-value problem is solved. The system of two partial differential equations of the fourth order that describes these
vibrations is analyzed in a vector-function space and is subjected to an equivalent transformation to obtain one vector equation
of the fourth order with two matrices as coefficients. One is an idempotent matrix; the other is a diagonal matrix. This makes
it much easier to construct a Cauchy vector function as an analytic function of these matrices
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 102–114, August 2007. 相似文献
12.
13.
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
14.
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
15.
Gao Yuanwen 《Acta Mechanica Solida Sinica》2007,20(2):180-188
An analysis of buckling/snapping and bending behaviors of magneto-elastic-plastic interaction and coupling for cantilever rectangular soft ferromagnetic plates is presented.Based on the expression of magnetic force from the variational principle of ferromagnetic plates,the buckling and bending theory of thin plates,the Mises yield criterion and the increment theory for plastic deformation,we establish a numerical code to quantitatively simulate the behaviors of the nonlinearly multi-fields coupling problems by the finite element method.Along with the phenom- ena of buckling/snapping and bending,or the characteristic curve of deflection versus magnitude of applied magnetic fields being numerically displayed,the critical loads of buckling/snapping, and the influences of plastic deformation and the width of plate on these critical loads,the plastic regions expanding with the magnitude of applied magnetic field,as well as the evolvement of deflection configuration of the plate are numerically obtained in a case study. 相似文献
16.
An extension of the Elastica theory is developed to study the large deflection of an elastic-perfectly plastic horizontal
cantilever beam subjected to a vertical concentrated force at its tip. The entire process is divided into four stages: I.elastic
in the whole cantilever; II.loading and developing of the plastic region; III.unloading in the plastic region; and IV.reverse
loading. Solutions for stages I and II are presented in a closed form. A combination of closed-form solution and numerical
integration is presented for stage III. Finally, stage IV is qualitatively studied. Computed results are given and compared
with those from small-deflection theory and from the Elastica theory. 相似文献
17.
Experiments on crack identification in cantilever beams 总被引:1,自引:0,他引:1
In this paper we present an experimental investigation of the identification of crack location and size. By providing the
first three natural frequencies through vibration measurements, curves of crack equivalent stiffness versus crack location
are plotted, and the intersection of the three curves predicts the crack location and size. In the experiments, the cracked
specimens were made using a wire-cut electrical discharge machine, and the cantilever beams were excited next to the free
end by means of an impulse force hammer. In order to obtain the accurate natural frequencies from the transient signal measured,
the method of zoom fast Fourier transform is adopted to improve frequency resolution. From experimental results, it is observed
that the identification errors of crack location and size are less than 2% and 4%, respectively. The effectiveness of crack
identification through vibration measurements is verified. 相似文献
18.
THEEXACTSOLUTIONFORTHICKLAMINATEDCANTILEVERCYLINDBICALSHELLFanJia-rang(范家让)(DepartmentofArchitecturalEngineering,HefeiUnivers... 相似文献
19.
热/均布载荷下双材料悬臂梁的解析解 总被引:1,自引:0,他引:1
基于弹性介质的二维本构关系和热传导理论,采用逆解法,研究了双材料悬臂梁在热/机械载荷作用下的问题,通过假设双材料悬臂梁构件的应力函数,利用应力、位移边界条件和连续性条件,给出了其位移、应力分布的表达式。 相似文献
20.
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