Effects of time delay on an active vibration control of a forced and Self-excited nonlinear beam

Loop delays are taken into our consideration when positive position feedback controller is used to control the vibrations of forced and self-excited nonlinear beam. External excitation is a harmonic excitation caused by support motion of the cantilever beam. Self-excitation is caused by fluid flow and modeled by a nonlinear damping with a negative linear part (Rayleigh’s function). The multiple timescales perturbation technique is applied to obtain a first-order approximate solution. Effects of time delay on the system are extensively studied, and optimal conditions for the system operation are deduced. The equilibrium solution curves are plotted for several values of controller parameters. The stability of the steady-state solution is investigated using frequency-response equations. The analytical results are validated by numerical integration of the original closed-loop system model equations, time histories and Poincaré map for the system. We realized that all predictions from analytical solutions are in good agreement with the numerical simulation.