TY - EJOU
AU - Wang, Xinzong
AU - Kang, Xiaofang
AU - Lei, Qingguan
TI - Chaotic Motion Analysis for a Coupled Magnetic-Flow-Mechanical Model of the Rectangular Conductive Thin Plate
T2 - Computer Modeling in Engineering \& Sciences
PY - 2023
VL - 137
IS - 2
SN - 1526-1506
AB - The chaotic motion behavior of the rectangular conductive thin plate that is simply supported on four sides by
airflow and mechanical external excitation in a magnetic field is studied. According to Kirchhoff ’s thin plate theory,
considering geometric nonlinearity and using the principle of virtual work, the nonlinear motion partial differential
equation of the rectangular conductive thin plate is deduced. Using the separate variable method and Galerkin’s
method, the system motion partial differential equation is converted into the general equation of the Duffing
equation; the Hamilton system is introduced, and the Melnikov function is used to analyze the Hamilton system,
and obtain the critical surface for the existence of chaos. The bifurcation diagram, phase portrait, time history
response and Poincaré map of the vibration system are obtained by numerical simulation, and the correctness is
demonstrated. The results show that when the ratio of external excitation amplitude to damping coefficient is higher
than the critical surface, the system will enter chaotic state. The chaotic motion of the rectangular conductive thin
plate is affected by different magnetic field distributions and airflow.
KW - Rectangular conductive thin plate; chaotic; airflow; magnetic field; Melnikov function; Galerkin’s method
DO - 10.32604/cmes.2023.027745