Vibration analysis of a magneto-elastic beam with general boundary conditions subjected to axial load and external force

In this study, the interactive behaviors among transverse magnetic fields, axial loads and external force of a magneto-elastic beam with general boundary conditions are investigated. The axial force and transverse magnetic force are assumed to be periodic with respect to time and two specified frequencies, one for axial force and the other for oscillating transverse magnetic field, are applied to the whole system. The equation of motion for the physical model is derived by using the Hamiltonʹs principle and the vibration analysis is performed by employing the characteristic orthogonal polynomials as well as the Galerkinʹs method. The displacement of the beam with the effect of the magnetic force, axial force and spring force are determined from the modal equations by using the Runge–Kutta method. Based on the present study, we can conclude that the effect of the magnetic field not only reduces the deflection but also decreases the natural frequencies of the system, also it should be noted that the specified beam model can be adopted to simulate several structures in mechanical, civil and electronic engineering.