转动薄壁圆柱筒振动特性:有限元法与解析解的对比

Vibration characteristics of rotating thin-walled cylindrical shell:comparison of finite element method with analytical solution

采用解析法和有限元法,研究了科氏力和离心刚化效应对不同约束条件下转动薄壁圆柱筒结构振动特性的影响,并进行了对比分析.结果表明,与解析解相比,有限元法计算得到的静止状态薄壁圆柱筒结构固有频率因边界条件不同而存在不同的差异,其中两端简支边界条件下与解析解吻合较好.随转速增加,前后行波频率差值加大,曲线明显分离,而这种分离趋势随周向波数的增大而减小.由于离心刚化效应的存在,相比于只考虑科氏力的影响,转动薄壁圆柱筒的行波频率有增大的趋势,并且当转速和周向波数较大时,前后行波频率均会大于对应的静频率.

Analytical solution and finite element method were used to study the influence of Coriolis force and centrifugal stiffening effect on the vibration characteristics of rotating thin-walled cylinder structure under different constraints. Results show that the finite element method to calculate the natural frequency of the thin-walled cylinder structure, com- pared with the analytical solution, has deviation under different static boundary conditions. Results of the two methods fit well for simply supported boundary conditions. With the increase of rotating speed, travelling wave frequency curves of backward wave and forward wave were clearly separated, and the trend of separation decreased with the increase of circ- umference wave number. Because of the influence of centrifugal stiffening effect, compared with to the case of only considering the effect of Coriolis force, the travelling wave frequency of rotating thin-walled cylindrical shell will increase, and when the rotating speed and circumference wave number is larger, the forward and backward traveling wave frequencies are greater than the static natural frequency.