The dynamic model and vibration suppression of a rotating cantilever beam under magnetic excitations are investigated in this article. The nonlinear constitutive relation of magnetostrictive materials is presented. The layout of the control system is demonstrated and explained. The kinetic energy, potential energy of the system, and work done by the electromagnetic force are obtained. The dynamic equations of the system are obtained and discretized by the Hamilton principle and Galerkin approach, respectively. Based on the negative feedback control method, the control scheme is implemented by the magnetostrictive layer. The dynamic model and control method are validated by the references. Various parameter values of the magnetic excitations and rotating beam systems are investigated to reveal their effects on the control behaviors of the bending vibration. Results illustrate that the magnetic excitations bring negative stiffness in the system and increase the responses of beam greatly. The magnetostrictive suppression is effective and can be regarded as the damping effect in the dynamic equations. Increasing the control gain, bias magnetic field and width ratio of the magnetostrictive layer to the controlled layer are beneficial to the vibration control. However, enlarging the angular velocity and pre-stress is harmful to the vibration suppression.
A dynamic model of a cantilever beam with a closed, embedded horizontal crack including local flexibilities at crack tips
