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在微尺度领域,材料力学性能存在尺度效应,使微梁动力学性态较传统宏观尺度柔性梁的动力学性态呈现明显不同.对固结于旋转刚环上内接微梁刚柔耦合动力学特性进行了研究,在精确描述微梁非线性变基础上,利用偶应力理论和Hamilton变分原理,在计入微梁由于横向变而引起的轴向变二耦合量条件下,推导出一次近似耦合模.首先忽略微梁纵向变影响,给出一次近似简化模,引入无量纲变量,对简化模做无量纲化处理,分析在非惯性系下内接微梁动力学响应,并与外接微梁进行比较;其次研究尺度效应对内接微梁动力特性影响.研究发现,与外接微梁只存在动力刚化效应不同,内接微梁还存在着动力柔化效应;本文给出了内接微梁无条件稳定临界径长比以及有条件稳定临界转速计算方法;尺度效应使微梁振动频率增大,振幅减小,提高了内接微梁失稳临界转速;随着模态断数增加,内接微梁失稳临界转速减小且有收敛值.
In the micro-scale field, the mechanical properties of materials have scale effect, which makes the dynamic behavior of the micro-beam significantly different from that of the traditional macro-scale flexible beam.For the rigid-flexible coupling dynamics of the internal micro-beam fixed on the rotating Rings Based on the accurate description of the nonlinear variation of the micro-beam, by using the theory of even-stress and Hamilton’s variation principle, an approximate coupling is deduced under the condition of the axial variation of the coupling due to lateral deformation of the micro-beam. Firstly, ignoring the influence of the longitudinal deformation of the micro-beam, an approximate simplified mode is given, dimensionless variables are introduced and the simplified mode is treated in a non-dimensional manner. The dynamic response of the inscribed micro-beam under non-inertial system is analyzed and compared with the external micro- And then study the effect of scale effect on the dynamic characteristics of the internal microbeam.The results show that there is only dynamic stiffening effect on the external microbeam, and the internal microbeam has the power softening effect. Beam unconditioned stable critical path length ratio and the method of calculating the critical speed of conditional stability. The scaling effect causes the vibration frequency of the micro-beam to increase and the amplitude decrease, which increases the critical rotational speed of the internal micro-beam instability. With the number of modal discontinuities Was added, then the micro beam instability is reduced and the critical speed convergence value.