CAJ | 학술논문

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。
침대공간장랍박막진면결구，용귀일화동태향응함수법학정박막변계궤하삼수대고유빈솔영향관계。용Bessel 함수작위박막횡향진동편미분방정적해，건립임의변계형상철단련통박막급복잡변계박막고유빈솔구해모형；침대평면장랍박막분별구해원형、L －형、분단원호변계고유빈솔；분석연구일정응력조건하변계궤하삼수대박막고유빈솔영향적내재관계。결과표명，변계형상도치박막면적감소、고유빈솔증가，반지역연。
For a kind of space pre-tensioned membrane structures,a dimensionless dynamic influential function method has been proposed,which can efficiently figure out the frequencies of arbitrarily shaped,homogeneous membranes with fixed boundaries.A model using the Bessel function as the solution to the partial differential equation for transverse vibration of thin membrane was established which can be used to calculate the natural frequencies of membrane with different radius of curvature and chord length.For planar pre-tensioned membrane,the natural frequencies of membrances with circular,L-shape and subdivided arc boundary conditions were calculated.On the condition of unchanged stresses, the relationships between the natural frequencies and boundary geometrical parameters of membrane were analysed.It is indicated that the boundary which makes the area of membrane larger matches higher frequencies and vice versa.