固支薄膜结构强非线性振动解析方法研究  

Analytical solutions to strongly nonlinear vibration of a clamped membrane structure

作　　者：李英民[1] 宋维举 王肖巍[1] LI Yingmin;SONG Weiju;WANG Xiaowei(College of Civil Engineering,Chongqing University,Chongqing 400045,China)

机构地区：[1]重庆大学土木工程学院

出　　处：《振动与冲击》2019年第17期144-148,177,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金(51478067);重庆市教委科学技术研究项目(KJ1723378)

摘　　要：膜结构刚度小,柔度大,在外荷载作用下的振动幅值一般大于自身膜材的厚度,且薄膜振动微分方程非线性项系数远大于1,属于强非线性振动系统。针对传统摄动方法和小挠度理论求解薄膜结构强非线性振动问题的局限性,将薄膜大挠度理论和改进多重尺度法结合,考虑膜材的几何非线性和振动阻尼的影响,求解平坦固支薄膜结构的强非线性振动控制方程,得到结构强非线性振动频率及位移函数解析式,并将结果与传统KBM摄动法解和没有考虑振动阻尼的精确级数解进行对比。为进一步验证理论方法的适用性,选用ZZF膜材进行振动特性试验,进一步验证改进多重尺度法对平坦固支薄膜结构强非线性振动研究的适用性。Due to a membrane’s small stiffness and large flexibility,its vibration amplitude under external loads is generally larger than its thickness,and its vibration equation’s nonlinear term coefficient is much larger than 1,so it belongs to a strongly nonlinear vibration system.Here,aiming at the limitation of the traditional perturbation method and the small deflection theory being used to solve strongly nonlinear vibration problems,the membrane large deflection theory was combined with the modified multi-scale method to solve the strongly nonlinear vibration governing equation of a flat clamped membrane structure considering effects of its geometric nonlinearity and vibration damping.The obtained results were compared with those of the accurate series solutions achieved using the traditional KBM method,etc.To verify the applicability of the proposed theoretical method,ZZF membrane material was adopted to conduct tests,and get membrane’s vibration characteristics.The test results showed that the modified multi-scale method is applicable for studying strongly nonlinear vibration of clamped membrane structures.

关 键 词：膜结构 强非线性振动 改进多重尺度法 幅频响应 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3