Abstract
Membrane materials are widely used in construction engineering with small mass and high flexibility, which presents strong geometric nonlinearity in vibration. In this paper, an improved multiscale perturbation method is used to solve the aerostatics stability of membrane roofs on closed and open structures by quantifying the effect of geometric nonlinearity on the single-mode aeroelastic instability wind velocity. Results show that the critical wind velocities of two models are smaller when the geometrical nonlinearity of the membrane material is neglected. In addition, under normal wind load, the influence of geometrical nonlinearity of the membrane on the aerodynamic stability of the roof can be neglected. However, under strong wind load, when the roof deformation reaches 3% of the span, the influence of geometric nonlinearity should be considered and the influence increases with the decrease of transverse and downwind span of the membrane roof. The results obtained in this paper have an important theoretical reference value for the design membrane structures.
Highlights
Fabric membrane is a widely used membrane material in construction engineering
Because of the small mass and flexibility, it is easy for vibration under external disturbance, and the stiffness of the membrane material is small, which results in the large vibration deformation of the membrane structure under wind load, showing strong geometric nonlinearity [3, 4]
In the mathematical analysis of aeroelastic instability of flexible membrane structures, Yang and Liu [7, 8] established the wind-induced dynamic coupling equation of hyperbolic parabolic membrane roof with small sag by using elastic shallow shell theory and ideal fluid potential flow theory in 2006 and determined the critical wind velocity of aeroelastic instability according to Routh–Hurwitz stability criterion. e influence of geometric nonlinearity of membranes was not considered when establishing the mathematical model
Summary
Fabric membrane is a widely used membrane material in construction engineering. It has the characteristics of high tensile strength and good flexibility. Because of the small mass and flexibility, it is easy for vibration under external disturbance, and the stiffness of the membrane material is small, which results in the large vibration deformation of the membrane structure under wind load, showing strong geometric nonlinearity [3, 4]. In the mathematical analysis of aeroelastic instability of flexible membrane structures, Yang and Liu [7, 8] established the wind-induced dynamic coupling equation of hyperbolic parabolic membrane roof with small sag by using elastic shallow shell theory and ideal fluid potential flow theory in 2006 and determined the critical wind velocity of aeroelastic instability according to Routh–Hurwitz stability criterion. In 2017, Liu et al [11] studied the aerodynamic stability of closed-tensioned membrane structures by the
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