Subharmonic and Ultra-Subharmonic Response of Nonlinear Elastic Beams Subjected to Harmonic Excitation
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摘要: 本文研究受横向周期载荷作用的梁的动力响应,梁的本构关系具有三次非线性项。轴向载荷作用下已屈曲的梁受到横向激励后,谐波是不稳定的,将分叉出次谐波、超次谐波,以Melnikov法确定了次谐轨道、超次谐轨道产生的条件。Abstract: In this paper the dynamics response of beams subjected to transverse harmonic excitation is studied.The nonlinearity of constitutive relations of the beam material is considered.When the buckled beams compressed by axial forces are subjected to transverse period perturbation,the harmonic bifurcates into subharmonic and ultra-subharmonic sequences.The critical conditions for subharmonic and ultra-subharmonic orbits are determined by use of Melnikov method.
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Key words:
- nonlinear /
- dynamic system /
- bifurcation
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[1] Tseng W Y, Dugunkjl J. Nonlinear vibrations of a beam under harmonic excitation[J]. J Appl Mech,1970,37(2):292~297. [2] Tseng W Y, Dugunkjl J. Nonlinear vibrations of a beam under harmonic excitation[J]. J Appl Mech,1971,38(1):467~476. [3] Baran Danida Dinca. Mathematical models used in studying the chaotic vibration of buckled beam[J]. Mechanics, Research Communications,1994,21(2):189~196. [4] Koch B P, Leven R W. Subharmonic and homoclinic bifurcation in a parametrically forced pendulum[J]. Physica D,1985,16:1~13.
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