Imperfect bifurcations in an initially curved plate loaded by incompressible axial airflow

摘要

This paper is concerned with the static bifurcations in a simply supported nonlinear curved plate subjected to a steady incompressible axial airflow. The fluid velocity potential of the flow is considered as the sum of two parts: One is due to the plate deformation, and the other is to the plate initial shape. The fluid force theoretically solved from the Bernoulli's equation has been successfully verified through a wind tunnel experiment. The von Karman's theory for large deflection of plates is used for the plate modeling. Results show that the plate loses symmetry and becomes imperfect due to its initial shape. The system has a fundamental and another two asymmetric bifurcated equilibrium solutions. Compared with the symmetric bifurcations in a flat plate, these bifurcations are called as the imperfect ones. The imperfect pitchfork-like bifurcation has a non-bifurcating branch and an additional imperfect bifurcation. The bifurcation regions and features are explored in detail in various parametric planes. There are two types of imperfect pitchfork-like bifurcations. The first type involves an additional saddle-node bifurcation and could be either supercritical or subcritical. However, the second type is associated with a transcritical-like bifurcation and represents the coexistence of both the supercritical and the subcritical bifurcations. The hysteresis in nature is due to the asymmetry of the system and can be restrained by increasing the tension and the fluid dynamic pressure.