基于波传播方法和多元分析的正交各向异性圆柱壳振动特性研究

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (7) : 227-232.

论文

汪志强，李学斌，黄利华

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Vibration characteristics of orthotropic circular cylindrical shells based on wave propagation approach and multi-variate analysis

WANG Zhiqiang , LI Xuebin , HUANG Lihua

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摘要

采用Flügge经典薄壳理论和波传播方法讨论了正交各向异性圆柱壳的自由振动问题。波传播法利用梁边界简化对应圆柱壳的边界条件，自由振动问题转换为求解关于圆频率的6次方程。通过参数化求解过程，获得了一定范围下正交各向异性圆柱壳自由振动的解空间。针对该空间应用多元统计方法讨论了圆柱壳的几何参数、材料特性参数对于频率的影响，分析了这些参数和频率的关联程度。基于方差分析讨论这些因素对频率的影响重要程度，并采用自组织映射技术研究了解空间的特性。本文给出的方法具有一般性，能够考虑正交各向异性圆柱壳在复杂边界和受外力的情况。

Abstract

Free vibration of orthotropic circular cylindrical shells was studied based on Flügge classical thin shell theory and the wave propagation approach. The shells’ boundary conditions were simplified using those of beams. The free vibration problem of the shells was converted into a 6-order algebraic equation for natural frequencies to be solved. Through parametrically solving the solution space for free vibration of orthotropic cylindrical shells was obtained. The multivariate statistical method was used to analyze effects of geometric parameters and material feature parameters of the shells on their natural frequencies, and correlations among these parameters and natural frequencies. ANOVA was used to discuss influence levels of these parameters on natural frequencies. A knowledge and data visualization approach named Self-Organizing Mapping (SOM) was adopted to study features of the solution space. A numerical example was presented here. The study provided a general method for further studying vibration characteristics of orthotropic circular cylindrical shells with complicated boundary conditions and external loads.

关键词

正交各向异性圆柱壳 / 自由振动 / 关联性分析 / 方差分析 / 自组织映射

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汪志强，李学斌，黄利华. 基于波传播方法和多元分析的正交各向异性圆柱壳振动特性研究[J]. 振动与冲击, 2018, 37(7): 227-232

WANG Zhiqiang,LI Xuebin,HUANG Lihua . Vibration characteristics of orthotropic circular cylindrical shells based on wave propagation approach and multi-variate analysis[J]. Journal of Vibration and Shock, 2018, 37(7): 227-232

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