弹性约束边界条件下矩形蜂窝夹芯板的自由振动分析  

Free Vibration Analysis of Rectangular Honeycomb-Cored Plates Under Elastically Constrained Boundary Conditions

作　　者：王永福 漆文凯[1] 沈承[2,3] WANG Yongfu;QI Wenkai;SHEN Cheng(College of Energy and Power Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,P.R.China;College of Aerospace Engineering,Nanjing University of Aeronautics andAstronautics,Nanjing 210016,P.R.China;State Key Laboratory for Strength and Vibration of Mechanical Structures,Xi’an Jiaotong University,Xi’an 710049,P.R.China)

机构地区：[1]南京航空航天大学能源与动力学院,南京210016 [2]南京航空航天大学航空学院,南京210016 [3]西安交通大学机械结构强度与振动国家重点实验室,西安710049

出　　处：《应用数学和力学》2019年第6期583-594,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11502110)~~

摘　　要：蜂窝夹芯板在飞行器、高速列车等领域有广泛的用途,对其开展振动分析具有明确的科学价值及工程意义.为区别于诸简支等传统约束边界,提出了弹性约束边界下蜂窝夹芯板结构的自由振动特性分析方法.具体来说,首先通过将蜂窝夹芯层等效为各向异性板,将夹芯板问题转变为三层板结构.进一步地,将板结构的位移场函数由改进的二维Fourier级数表示,并基于能量原理的Rayleigh-Ritz法得到结构的固有频率和固有振型,理论预测结果与数值模拟分析吻合较好.提出的理论模型可用于系统讨论约束边界对蜂窝夹芯结构自由振动特性的影响,为此类结构的约束方案设计提供理论依据.Honeycomb-cored plates are widely used in aircraft,high-speed trains and other fields,with clear scientific value and engineering significance worthy of vibration analysis.Other than classical boundary condition assumptions(such as simple supports),the elastic constraints were considered to analyze the free vibration characteristics of honeycomb-cored plates.Specifically,the sandwich plate problem was transformed into a 3-layer structure with the honeycomb core layer simplified as an equivalent anisotropic layer.Furthermore,the displacement field function for the structure was expressed in the form of the improved 2D Fourier series,and the natural frequencies and modal shapes of the structure were derived with the Rayleigh-Ritz method based on the energy principle.The theoretical results are in good agreement with the numerical ones.The proposed theoretical model can be used to systematically discuss the effects of boundary constraints on the free vibration characteristics of honeycomb-cored plates,and provides a theoretical basis for the design of constraint schemes for this kind of structures.

关 键 词：蜂窝夹芯板 弹性约束边界 二维Fourier级数 自由振动 

分 类 号：O34[理学—固体力学]