含迟滞力约束悬臂梁的非线性振动研究
收稿日期: 2013-01-28
修回日期: 2013-03-25
网络出版日期: 2013-04-25
基金资助
国家自然科学基金（51375109）;中国博士后科学基金（2012M510971）;哈尔滨工业大学科研创新基金（HIT.NSRIF.2014027）;黑龙江省博士后基金（LBH-Z11185）
Nonlinear Vibration of a Cantilever Beam Constrained by a Hysteresis Force
Received date: 2013-01-28
Revised date: 2013-03-25
Online published: 2013-04-25
Supported by
National Natural Science Foundation of China (51375109);China Postdoctoral Science Foundation (2012M510971);Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (HIT.NSRIF.2014027);Postdoctoral Science Foundation of Heilongjiang Province (LBH-Z11185)
为获得机械连接处微滑移对结构动力学行为的影响，以一自由端存在迟滞力约束的悬臂梁为研究对象，分析了其在基础激励下的主共振。约束端的迟滞力用Iwan模型描述，用多尺度法求得了此非线性边界条件下梁方程主共振过程中的稳态响应。通过可解性条件确定了稳态响应的幅频关系，并基于Lyapunov线性化稳定理论对稳态响应进行了稳定性分析。算例结果表明，主共振幅频曲线的共振峰均向左弯曲，表现出"软化"特征;当方程参数取值在特定范围时，幅频曲线以及响应振幅与激励幅值关系曲线均出现了不稳定部分，幅频曲线中不稳定部分的存在范围受激励幅值、黏性阻尼和约束刚度等参数影响。
张相盟 , 王本利 , 刘源 . 含迟滞力约束悬臂梁的非线性振动研究[J]. 航空学报, 2013 , 34(11) : 2539 -2549 . DOI: 10.7527/S1000-6893.2013.0184
To study the effects of microslip of mechnical joints on the structural dynamic behaviors of a structure with mechanical joints, the primary resonance of a base excitated cantilever beam with a hysteresis force constraining at the free end is analyzed in this paper. The hysteresis constraint is constructed by an Iwan model, and the method of multiple scales is applied to determine the steady-state response for the primary resonance of the governing equation of the beam with this nonlinear boundary condition. The nonlinear amplitude-frequency relationship of the steady-state response is derived from the solvability condition, and the stability of the steady-state response is analyzed by the Lyapunov-linearized stability theory. The results of the examples show that all the resonance peaks are left-bended as expected, exhibiting a softening effect. When the parameters of the equation are within a certain range, an unstable branch arises in each of the amplitude-frequency curves and the relationship curves of response amplitude vs excitation amplitude. It is found that the scope of the unstable branch of the amplitude-frequency curve is influenced by the parameters of excitation amplitude, viscous damping and constraint stiffness.
Key words： hysteresis; beam; multiple scales; primary resonance; stability
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