摘要
在考虑材料的非线性本构关系基础上,建立了非线性材料柱在轴向激励下纵向振动的非线性动力方程,采用谐波平衡方法求得了非线性材料柱在轴向激励下的1/2亚谐共振的近似解,并讨论分析了非线性材料柱在轴向激励下的1/2亚谐共振周期解的稳定性,给出了其动力不稳定的条件.经讨论分析可知:随着轴向激励力振幅的增大,非线性材料柱1/2亚谐共振的振幅、共振区域、不稳定区域也增大;随着非线性材料柱的横截面积的增大,非线性材料柱1/2亚谐共振的振幅、不稳定区域将减小,共振区域则增大.
The nonlinear dynamic equation was found for longitudinal vibration of nonlinear material column under axial excitation on the base of considering the nonlinear constitutive relation for the materials, approximate solution for 1/2 subharmonic resonance of nonlinear material column under axial excitation was obtained by harmonic balance method, and the stability was discussed for periodic solution by 1/2 subharmonic resonance of nonlinear material column under axial excitation, then the dynamic instability conditions for nonlinear material column was put forward. The analysis indicates that the 1/2 subharmonic resonance amplitude of nonlinear material column, the resonance region, and the unstable region increase along with the axial excitation of column increasing, and the 1/2 subharmonic resonance amplitude and the unstable region decrease, while the resonance region increase along with the cross sectional area of column increasing.
出处
《湖南文理学院学报（自然科学版）》
CAS
2009年第4期27-29,共3页
Journal of Hunan University of Arts and Science(Science and Technology)
关键词
非线性
柱
轴向激励
亚谐共振
nonlinearity
column
axial excitation
subharmonic resonance
