旋转SMA纤维混杂复合材料薄壁梁的自由振动  

FREE VIBRATION ANALYSIS OF ROTATING COMPOSITE THIN-WALLED CLOSED-SECTION BEAMS WITH SMA FIBERS

作　　者：任勇生[1] 杜向红[1] 姚文莉[2] 杨树莲[3] 

机构地区：[1]山东科技大学机械电子工程学院,青岛266510 [2]青岛理工大学理学院,青岛266033 [3]山东工商学院,烟台264005

出　　处：《固体力学学报》2011年第3期258-276,共19页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(10972124;10872118);山东省自然科学基金项目(Y2006F37)资助

摘　　要：研究具有SMA主动纤维的旋转复合材料单闭室薄壁截面梁的耦合自由振动问题.基于Hamilton原理并结合SMA纤维复合材料薄壁梁的二维截面内力(矩)与位移(转角)关系方程,导出旋转单闭室截面薄壁复合材料梁的1D耦合自由振动分析模型.该模型还考虑薄壁梁调矩角和预锥角的作用.采用Galerkin法求解振动模型,获得梁耦合振动固有频率的近似解.将本文建立的模型与计算方法,应用在周向均匀刚度配置(CUS)构型和周向反对称刚度配置(CAS)两种典型的复合材料薄壁的振动分析,获得了挥舞-摆振耦合、解耦扭转振动以及挥舞-摆振-扭转耦合振动固有频率近似解.通过数值计算揭示了SMA纤维含量与初始应变、铺层角、旋转速度、调矩角以及预锥角对各种耦合形式的振动固有频率的影响规律.The free vibration model of a rotating composite thin-walled closed-section beams with SMA fiber actuation is presented in this paper.The structural modeling is split into two parts： a two-dimensional analysis over the cross section,and a linear analysis of a beam along the beam span.The two-dimensional cross-sectional analysis is based on the force-deformation relationships equations,accounting for the presence of active SMA fibers distributed along the cross-section of the beam.Hamilton＇s principle is employed to derive the equations of motion and associated boundary conditions of the beams.The model includes anisotropy,pitch and precone angle.The Galerkin method is employed in order to solve the coupled differential equations.Numerical results are obtained for two cantilevered box beam： Circumferentially Uniform Stiffness（CUS） and Circumferentially Antisymmetric Stiffness（CAS）,the effects of the volume fraction of the SMA fiber,the martensitic residual strain,the fiber orientation,pitch and precone on the natural frequencies associated with coupled vibration modes are investigated.

关 键 词：SMA纤维 旋转梁 耦合振动 薄壁梁 调矩角 预锥角 

分 类 号：O327[理学—一般力学与力学基础]