Non-linear vibration of bimaterial magneto-elastic cantilever beam with thermal loading

作者：Wu Guan Yuan^*

来源：International Journal of Non-Linear Mechanics, 2013, 55: 10-18.

DOI：10.1016/j.ijnonlinmec.2013.04.009

• Vibration
• Dynamic instability
• Magneto-elastic
• Bimaterial cantilever beam
• Incremental harmonic balance (IHB) method
• Thermal load

Formulas and numerical results are studied for the transient vibration and dynamic instability of a bimaterial magneto-elastic cantilever beam which is subjected to alternating magnetic field and thermal loading. Materials are assumed isotropic, and the physical properties are assumed to have unique values in each layer. The governing equation of motion is derived by the extended Hamilton's principle, 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 the Euler-Bernoulli beam theory. The axial stresses results are found to be in good agreement with some known numerical solutions. Using Galerkin's 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 transient vibration and dynamic instability of the system are influenced by the magnetic field, the thickness ratio, the excitation frequency, but not by the temperature increase in this study.

• 出版日期2013-10