针对空间张拉薄膜阵面结构，用归一化动态响应函数法确定薄膜边界几何参数对固有频率影响关系。用Bessel函数作为薄膜横向振动偏微分方程的解，建立任意边界形状凸单连通薄膜及复杂边界薄膜固有频率求解模型；针对平面张拉薄膜分别求解圆形、L-形、分段圆弧边界固有频率；分析研究一定应力条件下边界几何参数对薄膜固有频率影响的内在关系。结果表明，边界形状导致薄膜面积减小、固有频率增加，反之亦然。
Abstract
For a kind of space pre-tensioned membrane structures, a non-dimensional dynamic influence function method is proposed by S.WKang, which can efficiently figure out the frequencies of arbitrarily shaped, homogeneous membranes with the fixed boundary. Firstly, a model using the Bessel function as the solution to the partial differential equation for transverse vibration of thin membrane is established which can be used to calculate the natural frequencies of membrane with different radius of curvature and chord length. Secondly, for planar pre-tensioned membrane, we calculate the natural frequencies of circular, L-shape and subdivide arc boundary of membranes. Finally, on the condition that stresses are unchanged, this paper analyzes the relationship between the natural frequencies and boundary geometrical parameters of membrane, and indicates that the boundary which makes the area of membrane larger matches higher frequencies, vice versa.
关键词
空间张拉薄膜结构 /
归一化动态响应函数 /
固有频率 /
有限元模型
{{custom_keyword}} /
Key words
space pre-tensioned membrane structure /
dimensionless dynamic influence function /
natural frequencies /
finite element model
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] Sakamoto H. Dynamic wrinkle reduction strategies for membrane structures[D]. Colorado: University of Colora- do, 2004.
[2] Sakamoto H,Park K C. Evaluation of membrane structure designs using boundary web cables for uniform- tensioning [J].ActaAstronautica,2007(60) :846-857.
[3] Leifer J, Belvin W K. Prediction of wrinkle amplitudes in thin film membranes using finite element modeling[C].The 44th AIAA/ASME/ASCE/AHS Structures, Structural dyna- mics, and material Conference, Norfolk, Virginia, 2003.
[4] Tessler A, Sleight D W, Wang J Y. [C]. The 44th AIAA/ASME/ASCE/AHS Structures, Structural dynamics, and material Conference, Norfolk, Virginia, 2003.
[5] 汪有伟,关富玲,韩克良,等.内外部悬索联合张拉膜结构的设计与分析[J]浙江大学学报:工学版,2010,44(6): 1213-1219.
WANG You-wei,GUAN Fu-ling,HAN Ke-liang,et al. Design and analysis of inner and outer cables suspendded membrane structures[J].Journal of Zhejiang University: Engineering Science ,2010,44(6):1213-1219.
[6] Kang S W, Lee J M, Kang Y J. Vibration analysis of arbitrarily shaped membranes using non-dimensional dynamic influence function[J]. Journal of Sound and Vibration,1999, 221:117-132.
[7] Kang S W, Lee J M. Application of free vibration analysis of membranes using the non-dimensional dynamic influence function[J].Journal of Sound and Vibration,2000, 234(3):455-470.
[8] Kang S W,Lee J M. Free vibration analysis of arbitrarily shaped plates with clamped edges using wave-type functions[J].Journal of Sound and Vibration,2002, 242(1): 9-26.
[9] 林文镜,陈树辉,李森.圆形薄膜自由振动的理论解[J].振动与冲击,2009,28(5):84-86.
LIN Wen-jing,CHEN Shu-hui,LI Sen.Analytical solution of the free vibration of circular membranc[J]. Journal of Vibration and Shock, 2009,28(5):84-86.
[10] 倪致祥. 数学物理方法[M].合肥：中国科学技术大学出版社,2012.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
PDF(1200 KB)
