Direct and parametric excitation of a nonlinear cantilever beam of varying orientation with time-delay state feedback

The primary and parametric resonances of a directly and parametrically excited nonlinear cantilever beam of varying orientation with time-delay in the linear state feedback are investigated. The time-delay is presented in the proportional feedback and the derivative feedback, respectively. The method of multiple scales is used to obtain the first-order approximation of response. The effect of the feedback gains and time-delay on the steady state responses of two type resonances is investigated. It is found that a proper selection of the feedback gains and time-delay can enhance the control performance.