【摘要】 综合考虑材料特性、几何特性和轴向载荷等因素的影响，对轴向运动变截面黏弹性功能梯度(functionally graded, FG)转轴的振动和稳定性演变进行了研究。基于Kelvin-Voight模型和Hamilton原理，建立了转轴的运动控制方程。采用Galerkin截断技术，推导出了系统的特征频率方程，并计算出了转轴横向挠曲振动的特征频率，进而分析了转轴系统的稳定性。确定了转轴系统的发散失稳及颤振失稳阈值，详细探究了轴向载荷、弹性模量梯度指数、密度梯度指数、锥形比、黏弹性参数等关键因素对转轴系统动力稳定性的影响。研究表明：FG材料与双陀螺连续体的结合使系统的动力学行为发生了显著变化，而考虑材料的黏弹性后转轴系统的稳定性演变历程变得更加复杂；弹性模量梯度参数和锥形比的增大可有效增强系统稳定性。更多还原

【Abstract】 The vibration and stability evolution of axially moving variable cross-section viscoelastic functionally graded(FG) spinning shafts were investigated in consideration of the effects of material properties, geometrical properties, and axial load. Based on the Kelvin-Voight model and Hamilton’s principle, the governing equations of motion of the shaft system were established. Using the Galerkin truncation technique, the eigenfrequency equation of the system was derived. As a result, the eigenfrequency of the transverse vibration of the shaft was calculated, and the stability of the system was analyzed. The divergence and flutter instability thresholds of the shaft system were determined, and the effects of key factors such as axial load, elastic modulus gradient index, density gradient index, taper ratio, and viscoelastic parameters on the dynamic stability of the shaft system were investigated in detail. The results show that the combination of FG material and double gyro continuum changes the dynamical behavior of the system significantly, and the stability evolution becomes more complicated after considering the viscoelasticity of the material. Also, the increase of the elastic modulus gradient parameter and the taper ratio can effectively enhance the stability of the system.更多还原