Estimation of wind-induced response of large membrane structures with nonlinear motion-induced aerodynamic force and nonlinear geometric stiffness

Abstract

Wind-induced dynamic response for large membrane structures with consideration of the coupling influences of nonlinear motion-induced aerodynamic force and nonlinear geometric stiffness is analytically evaluated in this study. By utilizing the equivalent nonlinear system approach, the Fokker-Planck-Kolmogorov equation of the membrane structures is derived, and the analytical response solutions, including probability density function, root-mean-square value, kurtosis, peak response, and peak factor, are presented. The accuracy of the proposed analytical solutions is checked by the numerical results obtained with the fourth-order Runge-Kutta approach. The findings reveal that vortex-induced vibrations occur at high wind speed regions due to the effect of nonlinear negative aerodynamic damping. Additionally, the geometric stiffness nonlinearity caused by large deformation is found to be significant for reducing the dynamic response amplitude in membrane structures. This study proposed herein presents an effective analytical approach for predicting the aero-elastic response of such flexible structures subjected to wind loads.