Frequency calculation method and wind-induced dynamic response of cable net façades considering the façade stiffness

In this study, a frequency formula for cable net façades that considers façade stiffness is proposed, and the effect of the façade stiffness on the dynamic behavior is analyzed. Initially, a theoretical formula based on membrane theory is derived for calculating the frequency of cable net façades while neglecting façade stiffness. Moreover, a total of 720 detailed finite element (FE) models of cable net façades with various parameters are established in ANSYS finite element software. The effects of glass thickness, cable spacing and cable force on frequency are analyzed with the detailed FE models. Based on the theoretical formula and detailed FE models, a fitted frequency formula that includes the façade stiffness is further proposed to calculate the first-order mode, which is the prominent mode. Furthermore, the effect of the façade stiffness on the dynamic response of the structure, including the cable force and displacement, is researched under excitation by wind loads based on time history analysis. The results show that the influence of façade stiffness on the frequency and dynamic response gradually decreases as the number of cable net grids increases. When the grid number is above 10, the impact can be ignored. In addition, the fitted formula can be used when the grid number is under 10, and when the number of grids exceeds 10, the theoretical formula can be applied. Considering this simplification, a simplified FE model is proposed in engineering design for grid numbers exceeding 10. When the grid number is less than 10, it is recommended to adopt a detailed FE model designed to avoid errors in structural design.