双叶片整体叶盘的非线性振动分析
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摘要
论文研究了双叶片整体叶盘的非线性振动问题,将双旋转叶片简化为弹簧-旋转曲壳系统,考虑叶片的预安装角和预扭转角的影响,利用Hamilton原理建立了整体叶盘的非线性偏微分运动方程.综合运用Galerkin方法和数值方法,对模型进行了非线性动力学分析,模拟不同转速和激励作用下的叶片运动,得到波形图、相位图和功率谱密度,讨论了转速和外载荷对系统的非线性动力学特性的影响.
The nonlinear vibration responses of the blisk with two blades were investigated in this paper. The two rotating blades were settled as a springs-rotating conical shells system,and the effects of the presetting and pre-twisted angles were considered for the model. Using Hamilton's principle, the partial differential governing equation of the motion of blisk was established. Galerkin's approach and numerical method were applied to analyze the nonlinear dynamics of the model. Numerical simulations were performed to investigate the responses of the blades under different rotating speeds and excitations. Numerical studies revealed the effects of the rotating speeds and excitations on the nonlinear vibration of the system.
The nonlinear vibration responses of the blisk with two blades were investigated in this paper. The two rotating blades were settled as a springs-rotating conical shells system,and the effects of the presetting and pre-twisted angles were considered for the model. Using Hamilton's principle, the partial differential governing equation of the motion of blisk was established. Galerkin's approach and numerical method were applied to analyze the nonlinear dynamics of the model. Numerical simulations were performed to investigate the responses of the blades under different rotating speeds and excitations. Numerical studies revealed the effects of the rotating speeds and excitations on the nonlinear vibration of the system.
引文
1 Rao J S,Carnegie W.Solution of the equations of motion of coupled bending-bending-torsion vibrations of turbine blades by the method of Ritz-Galerkin.International Journal of Mechanical Science,1970,12(10):875～882
2 Christensen E R,Lee S W.Nonlinear finite element modeling of the dynamics of unrestrained flexible structures.Computers and Structures,1986,23(6):819～829
3 晏水平,黄树红,韩守木.利用Euler梁模型计算汽轮机叶片静频和动频的传递矩阵法.中国电机工程学报,2000,20(6):68～70 (Yan S P,Huang S H,Han S M.Tansfer matrix methods of static and dynamic frequencies calculation for turbine blades by using Euler beam model.Proceedings of the CSEE,2000,20(6):68～70 (in Chinese))
4 Yao M H,Chen Y P,Zhang W.Nonlinear vibrations of blade with varying rotating speed.Nonlinear Dynamics,2012,68(4):487～504
5 Xiao S F,Chen B.Dynamic behavior of thin rectangular plate attached to moving rigid.Applied Mathematics and Mechanics,2006,27(4):555～566
6 Hu X X,Tsuiji T.Free vibration analysis of rotation twisted cylindrical thin panels.Journal of Sound and Vibration,1999,222(2):209～224
7 吴根勇,和兴锁,邓峰岩.旋转复合材料板的动力学性能研究.振动与冲击,2008(8):149～154 (Wu G Y,He X S,Deng F Y.Dynamic analysis of a rotating composite plate.Journal of Vibration and Shock,2008(8):149～154 (in Chinese))
8 Farhadi S,Hosseini-Hashemi S H.Aeroelastic behavior of cantilevered rotating rectangular plates.International Journal of Mechanical Sciences,2011,53(4):316～328
9 邓军,陈国平.匀速旋转弹性薄板分布动载荷时域识别.振动、测试与诊断,2011,31(6):724～727 (Deng J,Chen G P.Time-identification of distributed dynamic load for uniform rotating plate.Journal of Vibration,Measurement & Diagnosis,2011,31(6):724～727 (in Chinese))
10 王晓峰,徐可君,秦海勤.航空发动机风扇转子试验器动力学特性研究.动力学与控制学报,2017,15(2):142～148 (Wang X F,Xu K J,Qin H Q.Study on dynamic characteristics of aeroengine fan rotor tester.Journal of Dynamics and Control,2017,15(2):142～148 (in Chinese))
11 Yang S W,Hao Y X,Zhang W,et al.Nonlinear dynamic behavior of functionally graded truncated conical shell under complex loads.International Journal of Bifurcation and Chaos,2015,25(2):233
2 Christensen E R,Lee S W.Nonlinear finite element modeling of the dynamics of unrestrained flexible structures.Computers and Structures,1986,23(6):819～829
3 晏水平,黄树红,韩守木.利用Euler梁模型计算汽轮机叶片静频和动频的传递矩阵法.中国电机工程学报,2000,20(6):68～70 (Yan S P,Huang S H,Han S M.Tansfer matrix methods of static and dynamic frequencies calculation for turbine blades by using Euler beam model.Proceedings of the CSEE,2000,20(6):68～70 (in Chinese))
4 Yao M H,Chen Y P,Zhang W.Nonlinear vibrations of blade with varying rotating speed.Nonlinear Dynamics,2012,68(4):487～504
5 Xiao S F,Chen B.Dynamic behavior of thin rectangular plate attached to moving rigid.Applied Mathematics and Mechanics,2006,27(4):555～566
6 Hu X X,Tsuiji T.Free vibration analysis of rotation twisted cylindrical thin panels.Journal of Sound and Vibration,1999,222(2):209～224
7 吴根勇,和兴锁,邓峰岩.旋转复合材料板的动力学性能研究.振动与冲击,2008(8):149～154 (Wu G Y,He X S,Deng F Y.Dynamic analysis of a rotating composite plate.Journal of Vibration and Shock,2008(8):149～154 (in Chinese))
8 Farhadi S,Hosseini-Hashemi S H.Aeroelastic behavior of cantilevered rotating rectangular plates.International Journal of Mechanical Sciences,2011,53(4):316～328
9 邓军,陈国平.匀速旋转弹性薄板分布动载荷时域识别.振动、测试与诊断,2011,31(6):724～727 (Deng J,Chen G P.Time-identification of distributed dynamic load for uniform rotating plate.Journal of Vibration,Measurement & Diagnosis,2011,31(6):724～727 (in Chinese))
10 王晓峰,徐可君,秦海勤.航空发动机风扇转子试验器动力学特性研究.动力学与控制学报,2017,15(2):142～148 (Wang X F,Xu K J,Qin H Q.Study on dynamic characteristics of aeroengine fan rotor tester.Journal of Dynamics and Control,2017,15(2):142～148 (in Chinese))
11 Yang S W,Hao Y X,Zhang W,et al.Nonlinear dynamic behavior of functionally graded truncated conical shell under complex loads.International Journal of Bifurcation and Chaos,2015,25(2):233