On bifurcations and chaos of a forced rectangular plate with large deflection loaded by subsonic airflow. (April 2021)

• Record Type: Journal Article
• Authors: Li, Peng; Wang, Zhuoxun; Zhang, Dechun; Yang, Yiren
• Is Part Of: Thin-walled structures. Volume 161(2021)
• Publication Date: 2021-04
• Subjects: Subsonic flow -- Rectangular plate -- Bifurcation structure -- Chaotic motions -- Threshold criteria; Thin-walled structures -- Periodicals; 690.1
• DOI: 10.1016/j.tws.2020.107421
• Languages: English
• ISSNs: 0263-8231

Abstract

Abstract: This paper aims at the bifurcations and chaotic motions of a harmonically driven rectangular plate subjected to a uniform incompressible subsonic airflow. The plate equation of motion is derived by considering the von Karman's large deflection and Kelvin's type damping of material. A Galerkin-type solution is applied for the plate stress function and the aerodynamic force. The governing partial differential equation of the system is transformed into ordinary differential equations using the Galerkin method. The divergence instability and the pitchfork-like bifurcation of the plate are explored by theoretical and numerical analysis. The bifurcations of fixed points and periodic motions are thoroughly analyzed. The periodic motions can experience symmetry breaking/restoring bifurcations, period-doubling bifurcations, and saddle–node-like bifurcations, which are vital to the transition between different types of motions. Two typical bifurcation processes feature the bifurcation structure. The first one describes the change between the small and the large periodic orbits; the second one refers to the change between various large periodic orbits. Two criteria are used to predict the chaotic motions, which play a significant role in the transition between the small-orbit and the large-orbit periodic motions. The first one is the classical Holmes–Melnikov's criterion, and the second one is an approximated criterion that is newly developed from the resonant-response analysis of a reduced system. Results show that the current criterion brings some noticeable improvements compared with Holmes–Melnikov's criterion. Highlights: A complete modeling of a periodically driven three dimensional plate with large deflection in subsonic flow is developed. The plate loses its stability by divergence and experiences various bifurcations of both fixed points and periodic motions. The bifurcation structure of system is featured by two typical changing processes of different types of periodic motions. An approximated criterion for prediction of chaos in the transition between the small-orbit and the large-orbit periodic motions is developed.