Nonlinear Vibration of a Viscoelastic Beam Subjected to Both Axial Forces and Transverse Magnetic Field

The transient vibrations of a viscoelastic beam subjected to both actions of an alternating uniform transverse magnetic field and an axial periodic force are investigated. First, the governing equation of motion is derived by Hamilton's principle including axial loads, magnetic force, magnetic couple, and transverse damping factor. Two frequencies of pulsating axial force and oscillating transverse magnetic field are considered. The transient amplitudes and velocities are determined from the modal equations by using Runge-Kutta method. The effects of the viscosity parameter, axial load and magnetic field on the transient amplitudes and vibration frequencies of the first mode are investigated by the research of digital simulation.