桨叶的组合共振理论建模与分析  

Theoretical Modeling and Analysis on the Combination Resonance of Rotating Blade

作　　者：李贞坤 程起有[1] 朱艳[1] 钱峰[1] 刘晨 代志雄 LI Zhen-kun;CHENG Qi-you;ZHU Yan;QIAN Feng;LIU Chen;DAI Zhi-xiong(Science and Technology on Rotorcraft Aeromechanics Laboratory,China Helicopter Research and Development Institute,Jiangxi Jingdezhen 333001,China)

机构地区：[1]中国直升机设计研究所直升机旋翼动力学重点实验室,江西景德镇333001

出　　处：《装备环境工程》2022年第6期76-84,共9页Equipment Environmental Engineering

基　　金：重点实验室基金(KT-JJ-WDFX)。

摘　　要：目的对直升机单片桨叶在2个激励力下的组合共振进行理论研究。方法桨叶以固定角速度旋转,视为旋转的细长悬臂梁,受2个不同频率的简谐激励力作用。首先基于哈密顿原理推导旋转梁控制方程,考虑几何大变形和非线性惯性。其次对方程无量纲化,并采用伽辽金法对控制方程进行离散,最后使用摄动法中的L-P法(Lindstedt-Poincare method)对无量纲方程进行求解。结果获得了组合共振产生条件,同时得到了组合共振下的稳态幅频响应和相应的时间历程图。进一步获得了超谐波/次谐波共振与组合共振同时发生的条件,并对组合共振进行了参数分析,探索了各个激励频率成分、阻尼和激振位置等对组合共振的影响。结论当2激励力满足2Ω_(1)±Ω_(2)=ω_(0)、2Ω_(2)±Ω_(1)=ω_(0)或1/2(Ω_(1)±Ω_(2))=ω_(0)其中之一时,旋转梁可能发生组合共振。组合共振响应中,自由振动成分占主导,存在超谐波共振时,组合共振振幅得到进一步增强。This paper is to theoretically investigate the combination resonance of a single helicopter rotating blade under two excitation forces.The blade rotates at a fixed angular velocity and is regarded as a rotating slender cantilever beam,which is subjected to two excitation forces with different frequencies.Firstly,the governing equations of the rotating beam are derived with the aid of Hamilton's variation principle,considering large geometric deformation and nonlinear inertia.Secondly,the equ-ations are dimensionless,and the governing equation is discretized by applying the Galerkin scheme.Finally,the L-P method(Lindstedt-Poincare method)in the perturbation approach is applied to solve the dimensionless equation.The conditions of combination resonance are obtained and the steady-state amplitude-frequency response curves,as well as the corresponding time history diagram under the combined resonance are obtained;further obtain the conditions for the simultaneous occurrence of super-harmonic/sub-harmonic resonance and combination resonance,and analyze the parameters of combination resonance to explore the influence of each excitation frequency component,damping and excitation position on the combination resonance.Results reveal that when the two excitation forces satisfy one of the conditions,2Ω_(1)±Ω_(2)=ω_(0),2Ω_(2)±Ω_(1)=ω_(0) or 1/2(Ω_(1)±Ω_(2))=ω_(0),the combination resonance may occur in the rotating beam;the free vibration part is dominant in combination resonance,and the combination resonance amplitude is further enhanced in the presence of super-harmonic resonance.

关 键 词：组合共振 非线性振动 旋转悬臂梁 L-P法 桨叶振动 摄动法 

分 类 号：TJ85[兵器科学与技术—武器系统与运用工程] V214.3[航空宇航科学与技术—航空宇航推进理论与工程]