基于Rayleigh-Ritz法的复合材料薄壁圆柱壳热屈曲和热模态分析

摘要：热环境中的结构受热效应等的影响，结构刚度会发生变化，进而结构振动模态对几何参数、材料参数等的敏感性也会改变。针对纤维增强复合材料圆柱壳，建立能量方程，计入面内热载荷对圆柱壳做功，使用Rayleigh-Ritz法求解屈曲温度及振动频率等，使用有限元法验证了计算模型的准确性。重点关注了不同的几何参数、铺设角度及铺设方式下温度对圆柱壳的振型的影响。研究结果表明振动模态越接近屈曲模态，温度对频率的影响越大，且各阶振型的周向波数不同，温度对振动频率的影响也不同；圆柱壳越厚或越短，基频振型的周向波数越多；温度小于0.95倍屈曲温度时，温度增加基本不改变基频的振型，但接近屈曲温度时，在某些铺设角度下，某些振型的频率下降至低于原基频，发生振型跃迁。

Thermal Buckling and Modal Analysis of Composite Thin-Cylindrical Shells Based on Rayleigh-Ritz Method

[Abstract] Under the influence of thermal effect, the stiffness of the structure will change, and the sensitivity of vibration mode to geometric parameters and material parameters will also change. For fiber reinforced composite cylindrical shells, the energy equation is established, and the work done by in-plane thermal load is taken into account, and the buckling temperature and vibration frequencies are solved by Rayleigh-Ritz method. The accuracy of the calculation model is verified by finite element method. The effects of temperature on the vibration modes of cylindrical shells are focused in different geometric parameters, laying angles. The results show that the closer the vibration mode is to the buckling mode, the greater the influence of temperature on the frequency, and the different circumferential wave number of each mode, the different influence of temperature on the vibration frequency. The thicker or shorter cylindrical shell, the more circumferential wave number of fundamental frequency mode. When the temperature is less than 0.95 times of the buckling temperature, the vibration mode of the fundamental frequency is basically unchanged when increase the temperature. However, near the buckling temperature, at some laying angles, the frequencies of some modes fall below the original fundamental frequency, and the mode transition occurs.