CAJ | 학술논문

对旋转悬臂柔性梁的刚柔耦合一次近似模型的频率转向和振型转换特性进行研究,在精确描述柔性梁非线性变形基础上,计入柔性梁由于横向变形而引起的纵向缩短项,即二阶非线性耦合变形量,利用Hamilton变分原理和Rayleigh-Ritz假设模态法,推导出考虑"动力刚化"效应的一次近似耦合模型.引入量纲一参量,对耦合模型做归一化处理,利用状态空间法求解考虑横纵耦合效应的悬臂梁的固有频率和模态振型.研究发现,耦合效应对旋转悬臂梁固有频率的影响随旋转角速度的增大而变大;相邻两阶模态间存在频率转向,并在转向的过程中伴随着振型转换;相隔多阶模态间存在传递性频率转向,并在转向传递过程中伴随着振型转移;相邻两阶模态间还存在多次频率转向.
대선전현비유성량적강유우합일차근사모형적빈솔전향화진형전환특성진행연구,재정학묘술유성량비선성변형기출상,계입유성량유우횡향변형이인기적종향축단항,즉이계비선성우합변형량,이용Hamilton변분원리화Rayleigh-Ritz가설모태법,추도출고필"동력강화"효응적일차근사우합모형.인입량강일삼량,대우합모형주귀일화처리,이용상태공간법구해고필횡종우합효응적현비량적고유빈솔화모태진형.연구발현,우합효응대선전현비량고유빈솔적영향수선전각속도적증대이변대;상린량계모태간존재빈솔전향,병재전향적과정중반수착진형전환;상격다계모태간존재전체성빈솔전향,병재전향전체과정중반수착진형전이;상린량계모태간환존재다차빈솔전향.
The frequency veering and mode shape interaction properties of the first-order approximation coupling model with rigid-flexible coupling effect of a rotating cantilever beam is studied. Based on the accurate description of non-linear deformation of the flexible beam, the first-order approximation coupling model with the dynamic stiffening terms are derived from Hamilton theory and Rayleigh-Ritz assumed mode method, taking the second-order coupling quantity of axial displacement caused by transverse displacement of the beam into account. The coupling model is transformed into dimensionless form in which dimensionless parameters are identified. The natural frequencies and mode shapes of the rotating cantilever beam with coupling effect are computed by using state space method. The results obtained in the investigation indicate that the influence of the coupling effect on the natural frequencies of the rotating cantilever beam becomes larger as the rotating speed increases. It is shown that besides the frequency veering phenomenon between adjacent two-mode accompanied by mode shape interaction, the transitive frequency veerings among multi-mode accompanied by mode shape shift of a rotating cantilever beam with coupling effect are found and must be further researched deeply. The multi-frequency veerings between an adjacent two-mode are also found.