Vibration reduction in a 2DOF twin-tail system to parametric excitations

The use of active feedback control strategy is a common way to stabilize and control dangerous vibrations in vibrating systems and structures, such as bridges, highways, buildings, space and aircrafts. These structures are distributed-parameter systems. Unfortunately, the existing vibrations control techniques, even for these simplified models, are fraught with numerical difficulties and engineering limitations. In this paper, a negative velocity feedback is added to the dynamical system of twin-tail aircraft, which is represented by two coupled second-order nonlinear differential equations having both quadratic and cubic nonlinearities. The system describes the vibration of an aircraft tail subjected to multi-parametric excitation forces. The method of multiple time scale perturbation is applied to solve the nonlinear differential equations and obtain approximate solutions up to the third order approximations. The stability of the system is investigated applying frequency response equations. The effects of the different parameters are studied numerically. Some different resonance cases are investigated. A comparison is made with the available published work.