Modeling and Bifurcation Analysis of the Centre Rigid-Body Mounted on an External Timoshenko Beam
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摘要: 对于中心刚体固结悬臂梁系统,当不考虑梁剪应力(即Euler-Bernoulli梁)影响时,匀速转动梁的平凡解是稳定的。而对于深梁,有必要考虑剪应力(即Timoshenko梁)的影响,此时其匀速转动平凡解将出现拉伸屈曲。为此采用广义Hamilton变分原理建立了中心刚体固结Timoshenko梁这类刚-柔耦合系统的非线性动力学模型,应用数值方法研究了匀速转动Timoshenko梁非线性系统的分岔特性,以及失稳的临界转速。
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关键词:
- 刚-柔耦合系统 /
- 转动Timoshenko梁 /
- 拉伸失稳
Abstract: For the system of the centre rigid-body mounted on an external cantilever beam,the equilibrium solution of the steadily rotating beam is stable if the effect of its shearing stress(i.e.the beam belongs to the Euler-Bernoulli type)is not considered.But for the deep beam,it is necessary to consider the effect of the shearing stress(i.e.the beam belongs to the Timoshenko type).In this case,the tension buckling of the equilibrium solution of the steadily rotating beam may occur.In the present work,using the general Hamilton Variation Principle,a nonlinear dynamic model of the rigid- flexible system with a centre rigid-body mounted on an external Timoshenko beam is established.The bifurcation regular of the steadily rotating Timoshenko beam is investigated by using numerical methods.Furthermore,the critical rotating velocity is also obtained. -
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