Stability analysis of an axially moving viscoelastic beam under transverse magnetic fields and thermal loads

Slender flexible structures in electronic devices and spacecraft usually operate in complex thermal and magnetic environments, in which the stability is greatly affected by the complex environments. In this paper, an analytical method is proposed to study the stability of an axially moving viscoelastic beam under transverse magnetic fields and thermal loads. Firstly, the nonlinear control equation of the axially moving viscoelastic beam is derived by using Hamilton principle, in which the effects of the thermal loads, magnetic field variations and nonlinear deformation of the beam are considered based on the principle of magnetoelasticity. Secondly, Galerkin's method was applied to the derived continuous model to obtain the discrete differential equations of each vibrating mode. Finally, the incremental harmonic balance (IHB) method was employed to determine the unstable regions in the parameter space. The influences of the thermal load, axially moving velocity of the beam, viscosity coefficient, and magnetic field intensity on the regions of stability are investigated. It is found that the thermal loads, axially moving velocity and magnetic field intensity exert a significant influence on the unstable region. The derived results take into account of the combined effects of magnetic field and thermal variation, which is beneficial in understanding the stability of axially moving beams under complex magnetic and thermal environment.