扭转弹簧约束复合材料层压梁的自由振动  

Free transverse vibration of composite laminated beam restrained by torsion springs

作　　者：陈庆远 李静[1] 方鹏亚 裴世勋 刘双燕 苏毅 CHEN Qingyuan;LI Jing;FANG Pengya;PEI Shixun;LIU Shuangyan;SU Yi(College of Aero Engine,Zhengzhou University of Aeronautics,Zhengzhou 450046,China)

机构地区：[1]郑州航空工业管理学院航空发动机学院,郑州450046

出　　处：《振动与冲击》2023年第13期170-176,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金(72001192);河南省自然科学基金(202300410490);河南省科技攻关项目(212102210438,222102210044,222102320337);河南省高校重点科研项目(22B460025)。

摘　　要：基于伽辽金法推导了扭转弹簧约束复合材料层压梁自由振动的显式解析解。当复合材料层压梁两端的扭转弹簧刚度系数相等时,层压梁的横向挠度函数由两端简支梁的振动特征函数和两端固支梁修正的振动特征函数线性组合而成;当复合材料层压梁两端的扭转弹簧刚度系数不相等时,层压梁的横向挠度函数则由简支-固支梁的振动特征函数,固支-简支梁修正的振动特征函数和两端固支梁修正的振动特征函数线性组合而成。所构造的横向挠度函数可以避免扭转弹簧约束复合材料层压梁的经典振动特征函数在高阶(≥11)模态时出现的数值不稳定现象;研究表明,给出的显式解析表达式能有效地对扭转弹簧约束复合材料层压梁的自由振动进行分析。Here,based on Galerkin method,the explicit analytical solution for free transverse vibration of composite laminated beam restrained by torsion springs was derived.When torsion spring stiffness coefficients at both ends of composite laminated beam were equal,its transverse deflection function was composed of linear combination of vibration eigen-functions of a both-end hinged beam and modified vibration eigen-functions of a both-end fixed beam.When torsional spring stiffness coefficients at both ends of composite laminated beam were not equal,its transverse deflection function was composed of linear combination of vibration eigen-functions of a hinged-fixed beam,modified vibration eigen-functions of a fixed-hinged beam and modified vibration eigen-functions of a both-end fixed beam.The transverse deflection function proposed here could avoid the numerical instability of classical vibration eigen-functions of higher order(≥11)modes for composite laminated beam restrained by torsion springs.The study showed that the proposed explicit analytical expression can effectively analyze free transverse vibration of composite laminated beam restrained by torsion springs.

关 键 词：自由振动 扭转弹簧约束 复合材料层压梁 伽辽金法 显式解析解 

分 类 号：O327[理学—一般力学与力学基础]