The Nonlinear Vibration Response of Umbrella-Shaped Membrane Structure Under Heavy Rainfall Loads

This paper investigates the vibration characteristics of tensioned umbrella-shaped membrane structures with complex curvature under heavy rainfall. To solve the geometrical problem of the complex curvature of a membrane surface, we set the rule of segmentation and simplify the shape by dividing it into multi-segment conical membranes. The generatrix becomes a polyline with a constant surface curvature in each segment, simplifying calculations. The equivalent uniform load of different rainfall intensity is determined by the theory of the stochastic process. The governing equations of the isotropic damped nonlinear forced vibration of membranes are established by using the theory of large deflection by von Karman and the principle of d’Alembert. The equations of the forced vibration of the membrane are solved by using Galerkin’s method and the small-parameter perturbation method, and the displacement function, vibration frequency, and acceleration of the membrane are obtained. At last, the influence of the height–span ratio, number of segments, pretension and load on membrane displacement, vibration frequency, and acceleration of the membrane surface are analyzed. Based on the above data, the general law of deformation of the umbrella-shaped membrane under heavy rainfall is obtained. Data and methods are provided for the design and construction of the membrane structure as a reference. Moreover, we propose methods to enhance calculation accuracy and streamline the computational process.