科研之友
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摘要
One buckled simply supported giant magnetostrictive material (GMM) thin film laminated beam model subject to axial magnetic excitations is proposed. The magnetostrictive force is simplified as a harmonic excitation. Applying the Hamilton principle and Galerkin approach the model is expressed as a one dimensional vibrating model with parametrical excitation. The multi-scales method is used to obtain the approximation of the solution when the vibration is around the buckled position and the amplitude of the oscillation is small. With the help of the undermined fundamental frequency method and normal form theory the Melnikov approach is improved to calculate more precise threshold value of the amplitude of excitation leading to chaos. The numerical simulation shows the performance of the new Melnikov approach is much better than the traditional way.
