Internal resonance of an axially moving unidirectional plate partially immersed in fluid under foundation displacement excitation

This paper studies characteristics of 1:3 internal resonances and its bifurcations for an axially moving unidirectional plate partially immersed in a fluid under foundation displacement excitation. The fluid is assumed to be inviscid and incompressible. Based on Von Kármán large deflection equations of thin plates, and consider the influences of axial movement of the plate, axial tension, fluid‐structure interaction and foundation displacement, nonlinear vibration equations of an axially moving plate are established. By applying the Galerkin technique, the vibration equations are discretized, and thus achieve nonlinear differential equations on mode coordinates. Due to the influence of foundation displacement, there are more than two excitation items in the mode equations. Moreover, excitation amplitude is not a constant value, but a function of excitation frequency. Adopting numerical method and approximate analysis method, the equations are solved, moreover frequency‐response curves and time histories under internal resonance system are also obtained, the stability of periodic solution is also discussed. Global bifurcation phenomenon of averaging equations is studied for 1:3 internal resonance system. Changing course of periodic solution of the system and its complex nonlinear dynamic characteristics are revealed through bifurcation diagrams and phase trajectory diagrams.