Theoretical Study On Forced Vibration Response Of Umbrella-shaped Membrane Under Heavy Rainfall

In the field of construction,membrane structure is widely used for its advantages of light weight,economic,environmental protection,unique shape,large span and high structural efficiency.The tensile membrane structure is designed by form finding and prestressed to bear the load.However,due to the lack of bending resistance,the membrane is very sensitive to the wind,rain,hail and other out-of-plane loads,which is easy to cause large deformation or crack of the membrane,resulting in structural damage.Therefore,to understand membrane’s mechanical response characteristics,we need to study the dynamic response of the membrane under the action of heavy rainfall.Umbrella-shaped membrane is widely used in practical engineering.In this paper,the vibration response of isotropic umbrella-shaped membrane under the action of heavy rainfall is studied theoretically.The main contents are as follows:The rotational surface with equal stress distribution is catenoid surface,so we use its geometry as the shape of umbrella membrane.The finite element analysis software ANSYS is used for shape finding calculation,which verifies the correctness of adopting catenary surface as the shape of umbrella-shaped membrane.Then,the vibration response of the umbrella-shaped membrane under heavy rainfall is theoretically deduced.The equivalent uniform impact load of different rainfall intensity is determined by the stochastic process theory,and the damped nonlinear forced vibration governing equations of the umbrella-shaped membrane with isotropic characteristics are established.In order to solve the problem of surface curvature complexity of umbrella-shaped membrane with catenoid shape,we determined its principle of segmentation,which was simplified as several segments of open conical membrane,and the surface curvature of each segment of membrane was constant.We ignore the influence of geometric errors caused by segmentation on the calculation results,and adopt the ETFE membrane with isotropic characteristics,considering its geometric nonlinearity.Based on the Galerkin method and small parameter perturbation method,the approximate analytical solution of displacement function of membrane surface is obtained after solving the governing equations,and the vibration frequency and acceleration of membrane surface are further obtained.In the case study,three different height-span ratios of 0.1,0.15 and 0.2 are considered.The umbrella membrane is divided into one segment,three segments,five and seven segments,and the displacement function of each segment is obtained.After calculation,the general laws of displacement,vibration frequency and acceleration at the midpoint of membrane span under different height-span ratio,pretension and rainstorm load are obtained.In addition,when the pretension force is not less than 2.25 k N,the difference between the calculation results when the umbrella membrane is divided into seven segments and five segments is less than 5%.Therefore,we think that the calculation results after the umbrella-shaped membrane is divided into at least seven sections can meet the demand.Based on the above research process,the catenoid type umbrella-shaped membrane with complex curvature is simplified as a combination of open conical membrane with constant curvature.The influence of different factors on the displacement,frequency and acceleration of membrane surface under heavy rainfall is analyzed.At the same time,the general law of the vibration deformation of the umbrella-shaped membrane under the action of the heavy rainfall is obtained,and some methods to further improve the accuracy of the calculation are put forward.