Vibration of magnetostrictive composite cantilever actuator

Abstract

The bending vibration of the composite cantilever beam with magnetostrictive layer is investigated to simulate the dynamic response of a magnetostrictive actuator. Based on Timoshenko beam theory and the standard square nonlinear constitutive relations of magnetostrictive materials, new governing equations for deflection and two rotations in two layers of beam were obtained by Hamilton’s principle. The analytic solutions of the problem are found by the means of the space-time variable separation technique and the general solution theory for system of ordinary differential equations. The numeric verification examples illustrates validity of both the new mathematical model and the presented solutions. Furthermore, the influence of the geometric and material parameters on natural frequencies of the beam is examined in details. The responses of deflection and stress in the action of excited magnetic field is analysed, and it confirms in theorical that the behavior of frequency multiplying observed from the reported experiments in the literatures is an inherent dynamic characteristic for nonlinearily magnetostrictive actuator. The further study indicates that such behavior could be suppressed by increasing the bias magnetic field. In addition, the magnetic flux density caused by effect of magnet-mechanical coupling are calculated for the magnetostrictive cantilever beam. This work contributes to understand the dynamic characteristics of magnetostrictive composite cantilever actuator. The developed model can be used to guide the design of the magnetostrictive composite cantilever actuator for promising applications in MEMS.