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该文针对复合材料变截面薄壁旋转轴在不同约束下的振动与稳定性问题,提出了一个动力学模型。基于变分渐进法和拉格朗日方程,推导了复合材料变截面薄壁转轴的自由振动方程。在转轴的结构模型中,综合考虑了扭转、拉伸和弯曲引起的截面翘曲的影响。采用伽辽金法,分析了截面按线性或者抛物线变化的变截面旋转轴的固有频率和临界转速,其中还考虑了一端固定一端自由和一端固定一端铰支两种边界条件以及复合材料铺层角的影响。此外,通过对比分析模型的计算结果与商用有限元软件ANSYS的结果,该文所提出的分析模型的有效性在一定程度上得到了验证。
In this paper, a dynamic model is proposed for the vibration and stability of thin-walled composite variable section thin-walled rotating shafts under different constraints. Based on the variational asymptotic method and the Lagrange equation, the free vibration equation of thin-walled composite shaft with variable section was deduced. In the structural model of the shaft, the effects of torsional, tensile and bending cross-sectional warping are considered. Galerkin method is adopted to analyze the natural frequency and critical speed of a rotating shaft with variable cross-section according to linear or parabolic cross-section. Two kinds of boundary conditions including one end free end and one end fixed end hinge are considered, Impact. In addition, the validity of the analytical model proposed in this paper has been verified to some extent by comparing the results of the calculation with those of the commercial finite element software ANSYS.