微尺度悬臂梁非线性振动实验研究与理论分析  

Experimental and theoretical study on the nonlinear vibration of cantilever microbeams

作　　者：李贞坤 程起有[1] 冯志壮 孙凤楠 何玉明[2] LI Zhenkun;CHENG Qiyou;FENG Zhizhuang;SUN Fengnan;HE Yuming(Science and Technology on Rotorcraft Aeromechanics Laboratory,China Helicopter Research and Development Institute,Jingdezhen 333001,Jiangxi,China;Department of Mechanics,Huazhong University of Science and Technology,Wuhan 430074,Hubei,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 [2]华中科技大学力学系,湖北武汉430074

出　　处：《实验力学》2021年第6期793-803,共11页Journal of Experimental Mechanics

基　　金：国家自然科学基金(11972013)资助。

摘　　要：为研究微梁非线性振动的尺度效应,采用前后扫频方式,针对不同厚度微尺度金属镍悬臂梁开展了主共振与超谐波共振实验研究,获得了各阶共振幅频特性曲线。建立了考虑几何大变形和非线性惯性效应的修正的偶应力Euler-Bernoulli悬臂梁模型,采用多尺度法中的多维Lindstedt-Poincaré法(多维L-P法)求解理论模型获得了各阶幅频响应方程,并分析了材料尺度常数、阻尼和激励力对系统的影响。通过理论结果与实验结果的对比,验证了微梁非线性振动的尺度效应。实验结果表明,微梁的主共振具有显著的软化特性,微梁的次共振中第二阶、第三阶、第四阶、第五阶和第六阶振动发生超谐波共振。The forward and backward frequency sweep method is employed to study the size effects of microbeams experimentally.Micro-scale nickel cantilever beams with different thicknesses are considered and the frequency-response curves of primary resonance and super-harmonic resonance of each order are obtained.To interpret the experimental phenomenon quantitatively,Euler-Bernoulli cantilever beam model considering large geometric deformation and nonlinear inertial effects was established,combined with the modified couple stress theory.The theoretical model was solved by the multi-dimension Lindstedt-Poincarémethod(multi-dimension L-P method),one of the perturbation methods,and the amplitude-frequency responses of various orders are acquired.In addition,the influence of material length scale parameter,damping,and excitation force on the system are discussed.The theoretical results were compared with the experimental results,the size effects of the nonlinear vibration of the microbeams are verified.The experimental results show that the primary resonance of the microbeam manifests significant softening characteristics,and super-harmonic resonance of orders two,three,four,five,and six are observed.

关 键 词：微尺度悬臂梁 非线性振动 振动实验 多维L-P法 

分 类 号：O322[理学—一般力学与力学基础]