论文部分内容阅读
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Ω(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。
The natural frequency of the rotating functionally graded cylindrical shell under free vibration with different volume fraction, axial wave number, circumferential wave number, material composition, geometric parameters and boundary conditions was studied. Based on Love first-order shell theory, the governing differential equations of rotating cylindrical shell are established, and the eigenvalue equations of free vibration natural frequency of rotating cylindrical shell are calculated. In order to verify the validity of this method, the frequency parameters of the isotropic non-rotating cylindrical shell S-S were calculated and compared with the existing literature to prove that there is a good agreement. The influence of the volume fraction on the free vibration of a rotating functionally graded cylindrical shell is studied by an example. The results show that axial wave number m, aspect ratio L / R, ratio of thickness to diameter h / R and boundary conditions have a great effect on the natural frequency; volume fraction and material composition have little effect; the natural frequency of the forward wave is larger than The natural frequency of the forward wave increases with the increase of the rotational speed Ω (rad / s). The natural frequency of the backward wave decreases with the increase of the rotational speed.