水下FG圆柱壳临界载荷和固有频率预测方法-《郑州大学学报(工学版)》

文章信息/Info

Title:: The prediction method for critical buckling pressure and natural frequency of submerged functionally graded cylindrical shell

Author(s):: Li Rong; Yang Meng; Liu Linxia; Liang Bin;; School of Civil Engineering, Henan University of Science and Technology;

Keywords:: Water function gradient cylindrical shell; flexion critical load; inherent frequency; static water pressure; predictive method

摘要:: 针对水下功能梯度(FG)圆柱壳振动预测方法的不足，本文提出了一种适用于水下FG圆柱壳的屈曲临界载荷和固有频率预测方法。采用Flügge理论和波动法建立静水压力下FG圆柱壳耦合振动特征方程，使用牛顿迭代法求出静水压力下FG圆柱壳的固有频率，进而得到FG圆柱壳固有频率的平方和静水压力呈线性关系这一重要结论。基于此结论，通过使用线性拟合方法，最少仅需三组固有频率数据即可在保证精确度的基础上快速建立静水压力下FG圆柱壳固有频率的趋势线方程，从而得到屈曲临界载荷预测值以及任意静水压力下固有频率预测值。通过多组算例对比分析，证明该方法预测结果与实际结果几乎完全一致，预测精度高，计算量小，便于实际应用。

Abstract:: In order to make up for the lake of prediction method for the vibration of submerged functionally graded (FG) cylindrical shell, a prediction method for the critical buckling pressure and natural frequency of submerged FG cylindrical shell is presented. The coupled vibration characteristic equation of system is established based on the Flügge theory and wave propagation method. The data of natural frequencies under different hydrostatic pressures can be obtained by solving this equation. The results show that the squared fundamental natural frequency of submerged FG cylindrical shell is linearly related to hydrostatic pressure. Based on this conclusion, the predicted values of critical buckling pressure can be obtained accurately by using only three data values of natural frequencies. In addition, the data of natural frequency for FG cylindrical shell under arbitrary hydrostatic pressure can be easily got by using this linear fitting method. The calculation results indicated that the predicted results coincide with the reference results. The validity and usefulness of the proposed method in engineering application is proved