中文摘要：

研究了不同体积分数、轴向波数、周向波数、材料组分、几何参数和边界条件下旋转功能梯度圆柱壳自由振动时的固有频率。基于Love一阶壳体理论建立旋转圆柱壳控制微分方程，计算出旋转功能梯度圆柱壳自由振动固有频率的特征方程。为验证该方法的有效性，计算了各向同性不旋转圆柱壳S-S时的频率参数，并与已有文献做了对比，经证明有较高的吻合度。通过算例，研究了体积分数等对旋转功能梯度圆柱壳自由振动的影响。结果表明：轴向波数m、长径比L/R、厚径比h/R和边界条件对固有频率的影响较大；体积分数、材料组分的影响较小；前向波的固有频率大于后向波；前向波的固有频率随转速赘（rad/s）的增大而增大；后向波的固有频率随转速的增大而减小。

英文摘要：

The effects of volume fraction, axial wave number, circumferential wave number, material components and boundary conditions on the free vibration of rotating functionally graded （FG） cylin-drical shells are studied. Based on Love’s first approximation theory, differential equation is built up, and then the shell eigenfrequency equation is derived. In order to verify the validity of the present method, the frequency parameters of simply supported isotropic non-rotating cylindrical shell are compared with the published results with good agreement. The effect of volume fraction, etc. on the natural frequencies is investigated by examples. It is found that axial wave number m, length/radius ratio L/R, thickness/radius ratio h/R, and boundary conditions have significant contributions to the natural frequencies, while volume fraction and constituent materials have low effects. The natural fre-quencies of the forward waves are bigger than the backward waves. With the increasing of rotating speeds ？ （rad/s）, the natural frequency of forward wave increases, while the frequency of backward waves reduces.