弹性约束边界条件下矩形蜂窝夹芯板的自由振动分析
|
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 2 D 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.
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 2 D 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.
引文
[1] 鲍四元,邓子辰.薄板弯曲自由振动问题的高精度近似解析解及改进研究[J].应用数学和力学,2016,37(11):1169-1180.(BAO Siyuan,DENG Zichen.High-precision approximate analytical solutions for free bending vibrations of thin plates and an improvement[J].Applied Mathematics and Mechanics.2016,37(11):1169-1180.(in Chinese))
[2] 冀伟,刘世忠,吴晖.四边简支正交各向异性蜂窝型夹层板固有频率计算[J].计算力学学报,2012,29(3):417-420.(JI Wei,LIU Shizhong,WU Hui.Natural frequency for rectangular orthotropic honeycomb sandwich plates with all edges simply supported[J].Chinese Journal of Computational Mechanics,2012,29(3):417-420.(in Chinese))
[3] 任树伟,辛锋先,卢天健.蜂窝层芯夹层板结构振动与传声特性研究[J].力学学报,2013,45(3):349-358.(REN Shuwei,XIN Fengxian,LU Tianjian.Vibroacoustic performance of simply supported honeycomb sandwich panels[J].Chinese Journal of Theoretical and Applied Mechanics,2013,45(3):349-358.(in Chinese))
[4] LEISSA A W.The free vibration of rectangular plates[J].Journal of Sound & Vibration,1973,31(3):257-293.
[5] WARBURTON G B.The vibrations of rectangular plates[J].Proceeding of the Institute of Mechanical Engineers(Series A),1954,168(1):371-384.
[6] DICKINSON S M,LI E K H.On the use of simply supported plate functions in the Rayleigh-Ritz method applied to the flexural vibration of rectangular plates[J].Journal of Sound and Vibration,1982,80(2):292-297.
[7] WARBURTON G B.Response using the Rayleigh-Ritz method[J].Journal of Earthquake Engineering and Structural Dynamics,1979,7(4):327-334.
[8] WARBURTON G B,EDNEY S L.Vibrations of rectangular plates with elastically restrained edges[J].Journal of Sound and Vibration,1984,95(4):537-552.
[9] LI W L.Vibration analysis of rectangular plates with general elastic boundary supports[J].Journal of Sound and Vibration,2004,273(3):619-635.
[10] KHOV H,LI W L,GIBSON R F.An accurate solution method for the static and dynamic deflections of orthotropic plates with general boundary conditions[J].Composite Structures,2009,90(4):474-481.
[11] DU J T,LI W L,LIU Z G,et al.Acoustic analysis of a rectangular cavity with general impedance boundary conditions[J].The Journal of the Acoustical Society of America,2011,130(2):807-817.
[12] JIN G,SU Z,SHI S S,et al.Three-dimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions[J].Composite Structures,2014,108:565-577.
[13] 梁森,陈花玲,陈天宁,等.蜂窝夹芯结构面内等效弹性参数的分析研究[J].航空材料学报,2004,24(3):26-31.(LIANG Sen,CHEN Hualing,CHEN Tianning,et al.Analytical study of the equivalent elastic parameters for a honeycomb core[J].Journal of Aeronautical Materials,2004,24(3):26-31.(in Chinese))
[14] 高涛,漆文凯,沈承.基于一种新的均匀化实施方法的FRP刚度预测[J].航空学报,2016,38(5):1-11.(GAO Tao,QI Wenkai,SHEN Cheng.Prediction of FRP stiffness based on a new implementation of homogenization method[J].Acta Aeronautica et Astronautica Sinica,2016,38(5):1-11.(in Chinese))
[15] 沈观林,胡更开.复合材料力学[M].北京:清华大学出版社.(SHEN Guanlin,HU Gengkai.Mechanics of Composite Material[M].Beijing:Tsinghua University Press.(in Chinese))
[2] 冀伟,刘世忠,吴晖.四边简支正交各向异性蜂窝型夹层板固有频率计算[J].计算力学学报,2012,29(3):417-420.(JI Wei,LIU Shizhong,WU Hui.Natural frequency for rectangular orthotropic honeycomb sandwich plates with all edges simply supported[J].Chinese Journal of Computational Mechanics,2012,29(3):417-420.(in Chinese))
[3] 任树伟,辛锋先,卢天健.蜂窝层芯夹层板结构振动与传声特性研究[J].力学学报,2013,45(3):349-358.(REN Shuwei,XIN Fengxian,LU Tianjian.Vibroacoustic performance of simply supported honeycomb sandwich panels[J].Chinese Journal of Theoretical and Applied Mechanics,2013,45(3):349-358.(in Chinese))
[4] LEISSA A W.The free vibration of rectangular plates[J].Journal of Sound & Vibration,1973,31(3):257-293.
[5] WARBURTON G B.The vibrations of rectangular plates[J].Proceeding of the Institute of Mechanical Engineers(Series A),1954,168(1):371-384.
[6] DICKINSON S M,LI E K H.On the use of simply supported plate functions in the Rayleigh-Ritz method applied to the flexural vibration of rectangular plates[J].Journal of Sound and Vibration,1982,80(2):292-297.
[7] WARBURTON G B.Response using the Rayleigh-Ritz method[J].Journal of Earthquake Engineering and Structural Dynamics,1979,7(4):327-334.
[8] WARBURTON G B,EDNEY S L.Vibrations of rectangular plates with elastically restrained edges[J].Journal of Sound and Vibration,1984,95(4):537-552.
[9] LI W L.Vibration analysis of rectangular plates with general elastic boundary supports[J].Journal of Sound and Vibration,2004,273(3):619-635.
[10] KHOV H,LI W L,GIBSON R F.An accurate solution method for the static and dynamic deflections of orthotropic plates with general boundary conditions[J].Composite Structures,2009,90(4):474-481.
[11] DU J T,LI W L,LIU Z G,et al.Acoustic analysis of a rectangular cavity with general impedance boundary conditions[J].The Journal of the Acoustical Society of America,2011,130(2):807-817.
[12] JIN G,SU Z,SHI S S,et al.Three-dimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions[J].Composite Structures,2014,108:565-577.
[13] 梁森,陈花玲,陈天宁,等.蜂窝夹芯结构面内等效弹性参数的分析研究[J].航空材料学报,2004,24(3):26-31.(LIANG Sen,CHEN Hualing,CHEN Tianning,et al.Analytical study of the equivalent elastic parameters for a honeycomb core[J].Journal of Aeronautical Materials,2004,24(3):26-31.(in Chinese))
[14] 高涛,漆文凯,沈承.基于一种新的均匀化实施方法的FRP刚度预测[J].航空学报,2016,38(5):1-11.(GAO Tao,QI Wenkai,SHEN Cheng.Prediction of FRP stiffness based on a new implementation of homogenization method[J].Acta Aeronautica et Astronautica Sinica,2016,38(5):1-11.(in Chinese))
[15] 沈观林,胡更开.复合材料力学[M].北京:清华大学出版社.(SHEN Guanlin,HU Gengkai.Mechanics of Composite Material[M].Beijing:Tsinghua University Press.(in Chinese))