Analytical Solution of the Nonlinear Vibration of the Steel Skeleton Supported Membrane Structure

Abstract

Abstract Steel skeleton supported membrane structure is the major structural form of membrane structure, accounting for more than 50%. The structural characteristics of membrane structure itself determine that the analysis of its self-vibration characteristics is very important in the design process. According to the von Karman’s large deflection theory and the D’Alembert’s principle, the governing equations of nonlinear viscous damping vibration of the skeleton supported orthotropic membrane structure were proposed. By applying the Galerkin method and the KBM perturbation means of obtaining the analytical solutions of frequency function, displacement function and mode function of damped nonlinear and linear free vibration of simply supported orthotropic membrane structures on four sides were obtained. In addition, it can be known by example analysis that the transverse stiffness of membrane structure can be improved by increasing prestress and rise span ratio in the practical engineering, and while the influence of geometrically nonlinear, orthotropic, damping and prestress on the dynamic feature of membrane structure must be fully considered. This paper provides some theoretical references for the wind-induced dynamic stability calculation and wind-resistant design of the steel skeleton supported membrane structure.