Study On Added Mass Of ETFE Cushions In Uniform Flow

In recent years,ETFE(Ethylene-Tetra-Fluoro-Ethylene)cushions are popularly used in the large-span space structure in civil engineering and the deployable structure in aerospace engineering,due to their light weight and rich styling.ETFE cushions are flexible structures and very sensitive to wind.Under wind,they suffer large dynamic responses,which greatly affect the surrounding flow field and cause a significant effect of added mass.So far,when studying the added mass of membranes under wind load,the literature has not considered the variation rule of the disturbance of the upper flow field along the direction of height caused by structure vibration.As a result,the theoretical formula established cannot reflect the added mass produced in the actual motion of the membrane.In addition,most of the theoretical studies on added mass in the literature focus on the structure of the tensioned membrane.The effect of added mass of inflated membrane such as ETFE cushions in uniform flow still remains untouched.Due to the difference in the load-bearing characteristics between ETFE cushions and tensioned membrane structures,it remains to be investigated whether the analytic formula of added mass of the tensioned membrane structure is suitable for the ETFE cushion.In the paper,the added mass produced by vibration of the ETFE cushion in uniform flow is deduced by combining theory with numerical method.In addition,the factors affecting the calculation accuracy of added mass are studied from the perspectives of still wind and uniform flow.The specific research contents and results are as follows:(1)With the help of ADINA,the internal gas filling and the flow field of closed structure are equivalent to the potential fluid to consider the influence of the added mass of the internal gas filling and the pneumatic stiffness of the closed flow field.They are combined with the external membrane material to build the structure model.The external flow field is equivalent to the uniform laminar flow field in the fluid module.The fluid-structure interaction(FSI)module in ADINA is used to realize the bidirectional coupling analysis between the structure and the flow field,and the effect of aerodynamic damping caused by energy dissipation is ignored in the analysis.Then,the time history of wind load obtained by FSI analysis is applied to the structure in reverse for computational structural dynamics(CSD)analysis.By comparing the nodal dynamicresponse results of FSI and CSD,the influence of added mass on the dynamic response of cushions was studied.The results indicate that the dynamic responses of the cushion from the FSI analysis are much smaller than those from the CFD/CSD analysis.It means that the effect of added mass has a significant effect on the dynamic behavior of ETFE cushions and should be considered in the numerical analysis.(2)The structure model is established by equating the internal gas filling,the closed flow field under the structure and the external flow field into potential fluid.The static wind coupling analysis of cushions is completed in the CSD module.By analyzing the coupling results,the variation rule of the disturbance of the upper flow field along the direction of height is explored.On the basis of considering the influence of the disturbance,according to the Laplace equation and the Bernoulli equation,the analytical expression of the added mass of the ETFE cushions in the homogeneous flow with low wind speed is derived by means of the energy conservation law.The correctness of the analytical method is verified by comparing the analysis results of FSI analysis and CSD analysis with added mass.The results indicate that when the structure vibrates,the additional air velocity is approximately distributed in the form of a simple quadric function along the height direction.The added mass solved according to the method in the paper can be well matched with the added mass generated in the coupled analysis of cushions.(3)In the case of still wind,the influence of structural parameters such as sagittal span ratio,curvature,initial internal pressure and side length on the calculation accuracy of added mass is studied by comparing the static wind coupling results with CSD analysis results after adding added mass.The results indicate that the calculation accuracy of added mass is better for the structure with higher sagittal span ratio,curvature and initial internal pressure,but the effect is not significant.For the ETFE cushion with larger side length,the calculation accuracy of added mass is worse.Its influence is more obvious than other parameters,but it is within the acceptable range.(4)In the case of uniform flow,the influence of parameters such as flow field wind speed,flow field wind direction,structural initial internal pressure and structural side length on the calculation accuracy of added mass is analyzed by comparing the results of FSI and CSD after adding added mass.The results indicate that the calculation accuracy of added mass is worse with the increase of wind speed,but the effect is not obvious.As the wind direction of the flow field increases,the calculation accuracy of the added mass at the position approaching the incoming flow direction becomes worse,and the calculation accuracy of the added mass at the position far from the incoming flow direction becomes better.However,on the whole,the influence of the wind direction of the flow field on the calculation accuracy of the added mass is not significant.The higher the initial internal pressure is,the better the calculation accuracy of added mass is,but the accuracy change is not obvious.Under the uniform inflow,the non-uniformity of the added mass distribution on the surface of cushions increases with the increase of the structure side length.The unevenness of added mass distribution can be corrected by the weighted average method.