通过结合非局部尺度和应变梯度效应的Mindlin板理论对轴对称旋转纳米圆板进行建模.考虑纳米圆板的剪切变形,应用非局部应变梯度理论推导出描述纳米板面外自由振动行为的控制微分运动方程.应用微分求积法对控制方程进行数值求解,从而得到旋转纳米板面外振动的固有频率.在数值算例中考虑了实际工程中常见的两种边界条件,即固定约束和简支约束.分析了固有频率随厚径比、角速度、非局部特征尺度和材料特征尺度的变化.特别地,旋转纳米圆板是否稳定的临界角速度是数值获得的.本研究对当前纳米技术和纳米器件中旋转圆形纳米结构的动态设计和控制具有参考意义.“,”A rotating axisymmetric circular nanoplate is modeled by the Mindlin plate theory. The Mindlin plate theory incorporates the nonlocal scale and strain gradient effects. The shear deformation of the circular nanoplate is considered and the nonlocal strain gradient theory is utilized to derive the governing differential equation of motion that describes the out-of-plane free vibration behaviors of the nanoplate. The differential quadrature method is used to solve the governing equation numerically,and the natural frequencies of the out-of-plane vibration of rotating nanoplates are obtained accordingly. Two kinds of boundary conditions are commonly used in practical engineering,namely the fixed and simply supported constraints,and are considered in numerical examples. The variations of natural frequencies with respect to the thickness to radius ratio,the angular velocity,the nonlocal characteristic scale and the material characteristic scale are analyzed in detail. In particular,the critical angular velocity that measures whether the rotating circular nanoplate is stable or not is obtained numerically. The presented study has reference significance for the dynamic design and control of rotating circular nanostructures in current nano-technologies and nano-devices.