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.
Key words
space pre-tensioned membrane structure /
dimensionless dynamic influence function /
natural frequencies /
finite element model
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