ACTA AERONAUTICAET ASTRONAUTICA SINICA >
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)
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
ZHANG Xiangmeng , WANG Benli , LIU Yuan . Nonlinear Vibration of a Cantilever Beam Constrained by a Hysteresis Force[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2013 , 34(11) : 2539 -2549 . DOI: 10.7527/S1000-6893.2013.0184
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