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

WANG Yongfu; QI Wenkai; SHEN Cheng

doi:10.21656/1000-0887.390348

Volume 40 Issue 6

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2019 > 40(6): 583-594

WANG Yongfu, QI Wenkai, SHEN Cheng. Free Vibration Analysis of Rectangular Honeycomb-Cored Plates Under Elastically Constrained Boundary Conditions[J]. Applied Mathematics and Mechanics, 2019, 40(6): 583-594. doi: 10.21656/1000-0887.390348

Citation:

PDF( 5356 KB)

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

doi: 10.21656/1000-0887.390348

¹College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R.China;²College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R.China;³State Key Laboratory for Strength and Vibration of Mechanical Structures,Xi’an Jiaotong University, Xi’an 710049, P.R.China

Funds: The National Natural Science Foundation of China（11502110）

Received Date: 2018-12-12
Rev Recd Date: 2019-04-30
Publish Date: 2019-06-01

Abstract

Abstract

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.
- honeycomb-cored plate,
- elastic constraint boundary,
- 2D Fourier series,
- free vibration

FullText(HTML)

References(15)

References

[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,〖STHZ〗 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,〖STHZ〗 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,〖STHZ〗 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,〖STHZ〗 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))