Based on the nonlocal strain gradient theory, the coupling nonlinear dynamic equations of a rotating double‐tapered cantilever Timoshenko nano‐beam are derived using the Hamilton principle. The equation of motion is discretized via the differential quadrature method. The effects of the angular velocity, nonlocal parameter, slenderness ratio, cross‐section parameter, and taper ratios are examined and discussed. It is shown that taper ratios and cross‐section parameter play a significant role in the vibration response of a rotating cantilever nano‐beam. Further as rotational angular velocity increases, the taper ratios and cross‐section parameter effect on the frequency response are increased for first modes of vibration.

中文翻译：

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基于非局部应变梯度理论的旋转双锥悬臂Timoshenko纳米梁的动力学分析

基于非局部应变梯度理论，利用汉密尔顿原理推导了旋转双锥悬臂Timoshenko纳米束的耦合非线性动力学方程。运动方程通过微分求积法离散化。检验并讨论了角速度，非局部参数，细长比，横截面参数和锥度比的影响。结果表明，锥度比和横截面参数在旋转悬臂纳米梁的振动响应中起着重要作用。此外，随着旋转角速度的增加，对于第一振动模式，锥度比和横截面参数对频率响应的影响也会增加。