边界几何参数对空间平面张拉膜结构固有频率影响研究

Natural frequencies of pre-tensioned membrane structure with different boundary geometrical parameters

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。

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.