The analysis of dynamic instability on the large amplitude vibrations of a beam with transverse magnetic fields and thermal loads

Abstract The dynamic instability of a pinned beam subjected to an alternating magnetic field and thermal load with the nonlinear strain, and made of physically nonlinear thermoelastic material has been studied. Applying the Hamilton's principle, the equation of motion with damping factor, induced current and thermal load is derived. Using the Galerkin's method, the governing equation is reduced to a time-dependent Mathieu equation. The incremental harmonic balance (IHB) method is applied to analyse the dynamic instability. The effects of non-dimensional parameters frequency ratio ( Ω ), load factor ( ϕ ), amplitude ( ‖ a ‖ ), damping factor ( k 1 ) and temperature increment (Δ T ) on the dynamic instability are obtained and discussed. Results show that the characteristics of magnetoelastic instability for the beam having the large deformation are distinctive from those of the beam having small deformation.

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