Nonlinear dynamic and time-delay vibration control of axially moving shape memory alloy plate immersed in fluid.

Given that the complicated dynamics induced by the fluid–solid interaction seriously restrict the structural engineering application when the axially moving plate is immersed in the fluid, we introduce the shape memory alloy materials to reconstruct the plates to improve the mechanical environment by studying the dynamical behavior and time-delay control problem of the system under external excitation. Considering that the liquid is an ideal case with no viscosity, rotation, and incompressibility, as well as the present system is influenced by the axial tension, the fluid–structure interaction, and the polynomial constitutive relationship of the shape memory alloy, the nonlinear governing equation of the axially motion of the thin plate is established based on the Hamilton's principle and the small deflection plate assumption. The Galerkin method is utilized to discretize the dynamic equation. The plate's equilibrium point is qualitatively analyzed, and the fourth-order Runge–Kutta method is used for numerical simulation. Using bifurcation diagrams, phase diagrams, and Poincare section diagrams, the nonlinear dynamic characteristics of the system are disclosed with varying the excitation amplitude. At the same time, the influence of the external load on the system's time-domain waveform is discussed. The multi-scale method is used to study the bifurcation behavior of the present plates in the case of primary resonance. By introducing the time-delay feedback method, the dynamic response of the system is controlled by selecting appropriate displacement and velocity time-delay parameters. Results show that the time-delay feedback controller can eliminate the jumping phenomenon and improve the system's stability, which further enhances the strength and reliability. [ABSTRACT FROM AUTHOR]