Affiliations: [a] School of Mechanical Engineering, Tianjin Polytechnic
University, Tianjin, China | [b] School of Mechanical Engineering , Tianjin University,
Tianjin, China | Université Laval, Canada | Tohoku University, Japan
Correspondence:
[*]
Corresponding author: Ge Gen, School of Mechanical Engineering,
Tianjin Polytechnic University, Tianjin 300160, China. E-mail:
[email protected]
Abstract: 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.
