Abstract
Abstract In order to study the influence of geometric nonlinearity and material parameters on the free vibration behavior of the cylindrical skeleton supported prestressed fabric composite membrane. In this paper, based on von Karman's large deflection theory and D’Alembert's principle, the governing equations of nonlinear viscous damped prestressed free vibration of frame supported anisotropic membrane structures were established. By using Galerkin and KBM perturbation method, the analytical expressions of frequency function, displacement function and mode shape of nonlinear free vibration were obtained. In order to verify the effectiveness and effective range of the method, the fourth order Runge-Kutta method was used for numerical calculation. The calculation examples of membrane material parameters were given. The calculation and analysis of different membrane prestress, different length width ratio, different rise span ratio and different material parameters (elastic modulus ratio, viscous damping and material density) were carried out. The results were compared with the numerical results obtained by Runge-Kutta method to verify the accuracy of the method. The research results of this paper provide a theoretical reference for the selection of membrane materials, the subsequent calculation of wind-induced stability of steel skeleton membrane structure and the design of wind-driven rain resistance.
Highlights
In order to study the influence of geometric nonlinearity and material parameters on the free vibration behavior of the cylindrical skeleton supported prestressed fabric composite membrane
The fourth order Runge-Kutta method was used to determine the effective range of the analytical solution, and a numerical example was given to verify it
(2) The nonlinear vibration of membrane is affected by the rise span ratio, prestress, elastic modulus ratio, viscous damping, length width ratios and material density
Summary
Abstract: In order to study the influence of geometric nonlinearity and material parameters on the free vibration behavior of the cylindrical skeleton supported prestressed fabric composite membrane. Influence of different material parameters on nonlinear vibration of the cylindrical skeleton | 191 of the modified Duffing ordinary differential equations for supported rectangular plates and shallow spherical shells, and found that the soft spring characteristic of the main chain curve was effective when the amplitude was small. Based on von Karman’s large deflection theory, Bubov-Galerkin method and KBM perturbation method, Liu et al [31, 32] studied the theory and numerical application of nonlinear forced vibration of anisotropy rectangular membrane and saddle membrane structures under impact load. The effects of different membrane prestress, different length width ratio, different rise span ratio and different membrane material parameters on the nonlinear free vibration of prestressed fabric composite membrane with cylindrical skeleton were analyzed by numerical examples, and some rules were obtained.
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