The analysis of dynamic instability of a bimaterial beam with alternating magnetic fields and thermal loads

In this study, the dynamic instabilities and transient vibrations of a bimaterial beam with alternating magnetic fields and thermal loads are investigated. Materials are assumed isotropic, and the physical properties are assumed to have unique values in each layer. Based on the Hamiltonʹs principle, the equation of motion is derived in which the damping factor, the electromagnetic force, the electromagnetic torque, and the thermal load are considered. The solution of thermal effect is obtained by superposing certain fundamental linear elastic stress states which are compatible with Euler Bernoulli beam theory. Using the Galerkinʹs method, the equation of motion is reduced to a time-dependent Mathieu equation. The numerical results of the regions of dynamic instability are determined by the incremental harmonic balance (IHB) method, and the transient vibratory behaviors are presented by the fourth-order Runge–Kutta method. The results show that the responses of the dynamic instability and transient vibrations of the system are influenced by the temperature increase, the magnetic field, the thickness ratio, the excitation frequency, and the dimensionless damping ratio. The effects of using different values of parameters are presented to display the instability and steady vibrations and reveal some interesting characteristics such as beats and resonance phenomenon.