摘要
采用二次摄动法研究了弹性梁在热膨胀状态下的横向非线性振动问题。首先,根据能量原理建立了大挠度梁的非线性振动方程,并对其进行量纲归一化;然后,采用二次摄动法将非线性方程进行离散,得到各阶摄动方程,逐阶求解其渐进解。算例结果表明:应用传统的摄动法(KBM)法分析大幅振动问题的偏差比较大,远不及应用二次摄动法得到的解准确;温度和振幅对梁的固有频率影响显著。
The nonlinear vibrations of elastic beam in the state of thermal expansion are analyzed with two-step perturbation method in this paper, Firstly, The non-linear large deflection differential equation of the roller supported beam is established by energy method, then, the nonlinear motion equation is nondimensionalized, and the nonlinear equation is solved by adopting the deflection function compatible to the boundary condition of the beam and by transforming the deflection function to a series of linear differential equations with two-step perturbation method. The higher-order asymptotic solution is obtained. Finally, analysis of example shows that natural frequency of the beam is closely related to the temperature changes and the amplitudes, and the inaccuracy occurred when KBM method is used to analyze the large amplitude vibration in the beam. The results obtained by KBM method proves to be much less accurate than the results presented by two-step perturbation method.
出处
《应用力学学报》
CAS
CSCD
北大核心
2015年第3期366-371,2,共6页
Chinese Journal of Applied Mechanics
